IGNOU BSCFMT BMTC 101 Introduction to Probability and Statistics Solved Assignment English

Looking for the solved assignment for BMTC 101 Introduction to Probability and Statistics? Here you can get the complete solved assignment in PDF format for your IGNOU course.

If you are preparing your assignment and need the answers in one place, this solved PDF can help you save time and understand how the questions can be answered. You can read it on your mobile, save it for later, or take a print if required.

BSCFMT 2026 - English

Before you order: Please check the course code, subject code, year and session with your assignment before purchasing.

BMTC 101: Introduction to Probability and Statistics

High Demand Verified Solution

★★★★★ 4.8/5 (32 Students)

₹80 ₹30

63% OFF You Save: ₹50

Language

Type

Choose Your Assignment (latest Selected) Check Question Included See Included Question

Title Name	IGNOU BSCFMT BMTC 101 Introduction to Probability and Statistics Solved Assignment English
Type	Soft Copy (E-Assignment) .pdf
University	IGNOU
Degree	BACHELOR DEGREE PROGRAMMES
Course Code	BSCFMT
Course Name	Bachelor of Science (Mathematics)
Subject Code	BMTC 101
Subject Name	Introduction to Probability and Statistics
Year	2026
Session	-
Language	English
Assignment Code	BMTC 101/Assignment-1/2026
Product Description	Assignment of BSCFMT (Bachelor of Science (Mathematics)) 2026. Latest BMTC 101 2026 Solved Assignment Solutions
Format	Ready-to-Print PDF (.soft copy)

Need Help With This Assignment?

Looking for the solved assignment for this subject? You can get the complete solved PDF and use it while preparing your assignment.

✓ Complete Solved Assignment — Questions with their answers in one PDF.

✓ Save Your Time — No need to search different websites for every question.

✓ Easy to Read — Keep the PDF on your phone or take a print when required.

✓ Get It Online — Download your assignment after successful payment.

✓ Useful for Preparation — Read the answers and prepare your assignment with less hassle.

Just check once before buying: Make sure the Course Code, Subject Code, Year and Session shown above match your assignment.

📋 Assignment Content Preview

Please make sure your assignment questions match your current IGNOU session

BMTC 101 2026 - English

Assignment
(To be done after studying all the blocks)

Course Code: BMTC-101
Assignment Code: BMTC-101/TMA/2026
Maximum Marks: 100

1. Which of the following statements are True or False? Give short proof or counter example in your answer.

i) If the correlation coefficient between X and Y is -0.8, then the correlation coefficient between 2X - 1 and -3Y - 1 is -0.48.

ii) If X and Y are independent binomial variates with parameters (n₁, p₁) and (n₂, p₂) respectively, then X + Y has binomial distribution with parameters (n₁ + n₂, p₁ + p₂).

iii) The function defined as
$$f(x) = \begin{cases} |x| ; & -1 < x < 1 \\ 0 ; & \text{otherwise} \end{cases}$
is a probability density function.

iv) For a normal distribution with mean $\mu$ and variance $\sigma^2$ , the hypotheses
$H_1 : \mu = \mu_0, \sigma^2 = 1$ and
$H_2 : \mu = \mu_0, \sigma^2 \ge 1$ are simple hypotheses.

v) In a problem of testing of a simple hypothesis against a simple alternative, if the probability of type-I error is known to be 0.06, then the power of the test will be 0.94.

2. The mean I.Q. of a large number of children of age 14 was 100 and standard deviation 16. Assuming that the distribution was normal, find

$\quad$ i) the percentage of children having I.Q. under 80.

ii) the limits in which the I.Q. of the middle 40% of the children will lie.

$\quad$ You may like to use the following values:

$\quad P(Z > 1.25) = 0.1056$

$\quad P(Z < -0.525) = 0.3$

3. 6 observations on (X, Y) yielded the following data:

$$\sum X_i = 30, \sum Y_i = 180, \sum X_i Y_i = 1000,$

$$\sum X_i^2 = 200, \sum Y_i^2 = 5642.$

$\quad$ i) Determine the correlation coefficient between X and Y.

ii) Given $X = 10$ , what will be the predicted value of Y?

iii) Given $Y = 15$ , what will be the predicted value of X?

4. A die is thrown 60 times with the following results:

Face of die	1	2	3	4	5	6
Frequency	8	7	12	8	14	11

Test that the die is unbiased at $5\%$ level of significance. Given that at 5, 6 and 7 d.f. the value of $\chi^2$ are 11.070, 15.592 and 14.067 respectively.

5. Consider the joint probability density function

$$f(x, y) = y^2 e^{-y(x+1)}; x \geq 0, y \geq 0.$

Are both x and y regressions linear? Give reasons for your answer.

6. a) The mean and standard deviation of a variable x are m and $\sigma$ respectively. Obtain the mean and standard deviation of $\frac{(ax+b)}{c}$ , where a, b and c are constants.

$\quad$ b) If X is a random variable such that $E(X) = 3$ and $E(X^2) = 13$ , determine a lower bound for P(-2 < X < 8).

7. a) Let E₁, E₂, E₃ and E₄ be arbitrary events. Write the following events in set notations:

$\quad$ i) not more than one of E₁, E₂, E₃, E₄.
$\quad$ ii) one and only one of E₁, E₂, E₃, E₄.
$\quad$ iii) E₁ and at least one of E₂, E₃, E₄.
$\quad$ iv) none of E₂, E₃ and E₄ using E₁.

$\quad$ b) Let the probability density function of r.v. X be
$$f(x) = \begin{cases} 1 + x & ; \ -1 < x \le 0 \\ 1 - x & ; \ 0 < x < 1 \\ 0 & ; \ \text{otherwise} \end{cases}$
$\quad$ and if $u = X$ and $v = X^2$ , find Cov(u, v). Also check the independence of u and v.

8. a) For a mesokurtic distribution with standard deviation 5, find fourth central moment m₄.

$\quad$ b) The probability that a card will have a flat tyre while crossing a certain bridge is 0.00005. Find the probability that, among 10,000 cars crossing the bridge,

$\quad$ i) exactly two cars will have a flat tyre.
$\quad$ ii) at most two cards will have a flat tyre.

9. a) Let X₁ be an observation from an exponential distribution with the p.d.f.

$$f(x) = \frac{1}{\theta} e^{-x/\theta}; x > 0$

Test the null hypothesis that the mean of the distribution is $\theta = 2$ against the alternative hypothesis that is $\theta = 5$ . The null hypothesis is accepted if and only if the observed value of the random variable is less than 3. Find the probabilities of type-I and type-II errors.

b) The mean and standard deviation of 20 items is found to be 10 and 2 respectively. At the time of checking it was found that one item having value 8 was incorrect. Calculate the mean and standard deviation if the wrong item is omitted.

10. a) Let X be a gamma variable with parameters αand λ, having E(X ) = 6 and Var(X ) = .3 Find αand λ. Also, find the m.g.f. of a gamma variable, and hence verify that mean of X is 6 and variance of X is 3 using m.g.f.

b) For married couples living in a certain locality, the probability that the husband will vote in a school board election is 0.21, the probability that they both will vote is 0.15. What is the probability that

i) at least one of them will vote?

ii) neither of them will vote?

BMTC 101 2026 - Hindi

सत्रीय कार्य

पाठ्यक्रम कोड: BMTC-101

सत्रीय कार्य कोड : BMTC-101/TMA/2026

अधिकतम अंक: 100

1. निम्नलिखित में से कौन-से कथन सत्य हैं और कौन-से असत्य? अपने उत्तर में संक्षिप्त उपपत्ति या प्रत्युदाहरण दीजिए। (10)

i) यदि X और Y के बीच सहसंबंध गुणांक -0.8 है, तो 2X - 1 और -3Y - 1 के बीच सहसंबंध गुणांक -0.48 होगा।

ii) यदि X और Y क्रमशः (n₁, p₁) और (n₂, p₂) प्राचलों वाले स्वतंत्र द्विपद चर हैं, तो X + Y प्राचल (n₁ + n₂, p₁ + p₂) वाला द्विपद बंटन होगा।

iii) $f(x) = \begin{cases} |x|, & -1 < x < 1 \\ 0, & \text{otherwise} \end{cases}$ द्वारा परिभाषित फलन एक प्रायिकता घनत्व फलन है।

iv) माध्य $\mu$ और प्रसरण $\sigma^2$ , वाले एक प्रसामान्य बंटन के लिए, परिकल्पनाएँ
$H_1 : \mu = \mu_0, \sigma^2 = 1$ और
$H_2 : \mu = \mu_0, \sigma^2 \ge 1$ सरल परिकल्पनाएँ हैं।

v) सरल वैकल्पिक के विरुद्ध सरल परिकल्पना के परीक्षण की समस्या में, यदि टाइप-I अशुद्धि की प्रायिकता 0.06 है, तो परीक्षण की क्षमता 0.94 होगी।

2. 14 वर्ष की आयु के बच्चों की एक बड़ी संख्या का माध्य I.Q. 100 और मानक विचलन 16 था। मान लीजिए कि बंटन प्रसामान्य था, तो निम्नलिखित ज्ञात कीजिए :

i) 80 से कम I.Q. वाले बच्चों का प्रतिशत।

ii) वह सीमा जिसके लिए बीच में 40% बच्चों की I.Q. होगी।

आप निम्नलिखित मानों का प्रयोग कर सकते हैं :

$P(Z > 1.25) = 0.1056$

$P(Z < -0.525) = 0.3$

3. (X, Y) पर किए गए 6 प्रेक्षणों से प्राप्त आँकड़े निम्नलिखित हैं :

$\sum X_i = 30, \sum Y_i = 180, \sum X_i Y_i = 1000,$

$\sum X_i^2 = 200, \sum Y_i^2 = 5642.$

i) X और Y के बीच सहसंबंध-गुणांक ज्ञात कीजिए।

ii) दिया गया है $X = 10$ , तब Y का प्रागुक्त मान क्या होगा?

iii) दिया गया है $Y = 15$ , तो X प्रागुक्त मान क्या होगा?

4. एक पासे को 60 बार फेंकने से निम्नलिखित परिणाम प्राप्त होते हैं :

पासे का मुख	1	2	3	4	5	6
बारम्बारता	8	7	12	8	14	11

5% सार्थकता स्तर पर परीक्षण कीजिए कि पासा अनभिनत है। दिया गया है कि 5, 6 और 7 स्वातंत्र्य कोटि के लिए $\chi^2$ के मान क्रमशः 11.070, 15.592 और 14.067 हैं।

5. निम्नलिखित संयुक्त प्रायिकता घनत्व फलन लीजिए :

$$f(x, y) = y^2 e^{-y(x+1)}; x \ge 0, y \ge 0.$

क्या दोनों x और y समाश्रयण रैखिक हैं? अपने उत्तर का कारण दीजिए।
6. a) एक चर x का माध्य और मानक विचलन क्रमशः m और $\sigma$ है। $\frac{(ax + b)}{c}$ , का माध्य और मानक विचलन ज्ञात कीजिए जबकि a, b और c अचर हैं।

b) यदि एक यादृच्छिक चर X इस प्रकार है कि $E(X) = 3$ और $E(X^2) = 13$ है, तो P(-2 < X < 8) का निम्न परिबंध ज्ञात कीजिए।

7. a) मान लीजिए कि E₁, E₂, E₃ और E₄ स्वैच्छिक घटनाएँ हैं। निम्नलिखित घटनाओं को समुच्चय संकेतनों में लिखिए:

i) E₁, E₂, E₃ और E₄ में एक से अधिक नहीं।

ii) E₁, E₂, E₃ और E₄ में से केवल एक।

iii) E₁ और कम-से-कम E₂, E₃, E₄ में से एक।

iv) E₁ के साथ E₂, E₃ और E₄ में से कोई नहीं।

b) मान लीजिए कि r.v. X का प्रायिकता घनत्व फलन निम्नलिखित है :

$f(x) = \begin{cases} 1 + x, & -1 < x \le 0 \\ 1 - x, & 0 < x < 1 \\ 0, & \text{otherwise} \end{cases}$
और यदि $u = X$ और $v = X^2$ हो, तो Cov(u, v) ज्ञात कीजिए। u और v के स्वातंत्र्य की भी जाँच कीजिए।

8. a) मानक विचलन 5 वाले मध्यककुदी बंटन के लिए चतुर्थ केंद्रीय आघूर्ण m₄ ज्ञात कीजिए।

b) किसी पुल को पार करते समय एक कार के टायर सपाट होने की प्रायिकता 0.00005 है। पुल पर करने वाली 10,000 कारों के लिए वह प्रायिकता ज्ञात कीजिए जबकि

i) ठीक 2 कारों के टायर सपाट होंगे।

ii) ज्यादा से ज्यादा 2 कारों के टायर सपाट होंगे।

9. a) मान लीजिए कि X₁ एक चरघातांकी बंटन का एक प्रेक्षण है, जिसका प्रायिकता घनत्व फलन

$$f(x) = \frac{1}{\theta} e^{-x/\theta}; x > 0$

है। निराकरणीय परिकल्पना कि बंटन का माध्य $\theta = 2$ है की प्रतिकूल वैकल्पिक परिकल्पना कि माध्य $\theta = 5$ है, का परीक्षण कीजिए। निराकरणीय परिकल्पना केवल तभी स्वीकार की जाती है यदि और केवल यदि यादृच्छिक चर का प्रेक्षित मान 3 से कम हो। टाइप-I और टाइप-II त्रुटियों की प्रायिकताएँ ज्ञात कीजिए।

b) 20 पदों का माध्य और मानक विचलन क्रमशः 10 और 2 पाया गया है। जाँच करते समय यह पाया गया कि मान 8 वाला एक पद गलत है। यदि गलत पद को हटा दिया जाए तो माध्य और मानक विचलन परिकलित कीजिए।

10. a) मान लीजिए X प्राचल $\alpha$ और $\lambda$ वाला एक गामा चर है जिसके $E(X) = 6$ और $Var(X) = 3$ हैं। $\alpha$ और $\lambda$ ज्ञात कीजिए। गामा चर का आघूर्ण जनक फलन भी ज्ञात कीजिए और इस प्रकार सिद्ध कीजिए कि आघूर्ण जनक फलन से X का माध्य 6 और X का प्रसरण 3 है।

b) एक मुहल्ले में रहने वाले वैवाहिक जोड़ों में, पति के एक स्कूल बोर्ड चुनाव में वोट देने की प्रायिकता 0.21 है, पत्नी के चुनाव में वोट देने की प्रायिकता 0.28 है और दोनों के वोट देने की प्रायिकता 0.15 है। इस बात की प्रायिकता क्या होगी कि

i) उनमें से कम से कम एक वोट देगा?

ii) उनमें से कोई भी वोट नहीं देगा?

❓ Frequently Asked Questions (FAQs)

Q: How will I receive the PDF?
A: Immediately after payment, the download link will appear.

Q: Is this hand-written or typed?
A: This is a professional typed computer PDF. You can use it as a reference for your handwritten submission.

➕Other Details

IGNOU BMTC 101 Solved Assignment 2026 – Prepare Smarter, Save Valuable Time

Searching for the 2026 IGNOU BMTC 101 Solved Assignment? Get a ready-to-use reference for BMTC 101 - Introduction to Probability and Statistics and make your assignment preparation simpler, faster and more organised. Our carefully prepared BMTC 101 Introduction to Probability and Statistics Solved Assignment is designed to help you understand the questions, study the important points and prepare your assignment answers with greater confidence.

Why spend hours searching through different sources when you can have your BMTC 101 solved assignment reference available in one convenient resource? Whether you are studying after work, preparing several IGNOU subjects together or simply want a dependable reference, this material can save you valuable preparation time.

BMTC 101 2026 Solved Assignment – What You Get

Latest 2026 assignment reference for BMTC 101 Introduction to Probability and Statistics
Question-wise answers arranged for easy study and reference
Clear and student-friendly presentation for easier understanding
English language version available
Digital soft copy / PDF for convenient access
Useful reference material for preparing your own assignment answers
Helps you identify important points, answer structure and relevant content

Stop Struggling With Every Question. Start Preparing With a Better Reference.

Assignment preparation can become time-consuming when you have multiple subjects, limited study hours and a long list of questions to complete. A good reference can help you move from “What should I write?” to “Now I understand how to prepare this answer.”

The IGNOU BMTC 101 Solved Assignment 2026 gives you a convenient study reference so you can review the questions, understand the expected subject matter and organise your own answers more efficiently.

Study less randomly. Prepare more systematically. Keep the reference with you while working on your assignment and use it whenever you need help understanding a question or arranging the important points.

Get Your BMTC 101 Introduction to Probability and Statistics Solved Assignment 2026

Course: Bachelor of Science (Mathematics) (BSCFMT)
Subject: BMTC 101 - Introduction to Probability and Statistics
Session: January 2026 - December 2026
Language: English

Need the Help Book / Solved Assignment?
Call us: 9199852182 / 9852900088
WhatsApp: 9199852182

Your Time Matters – Make Assignment Preparation Easier

If you are balancing IGNOU studies, work, family responsibilities or other subjects, every hour of study matters. Having a structured reference beside you can make it easier to understand the assignment and focus your time on preparing your own submission.

Instead of repeatedly searching for answers across different websites and sources, keep your BMTC 101 Introduction to Probability and Statistics Solved Assignment 2026 ready for reference whenever you study.

A Useful Reference for Your IGNOU Assignment Preparation

Understand the question → Find the relevant points → Study the answer → Prepare your own assignment with confidence.

IGNOU BSCFMT Assignments 2026

The BSCFMT (Bachelor of Science (Mathematics)) programme includes assignment work as part of the academic requirements applicable to students. Students should always verify the latest assignment questions, instructions and submission requirements from the official IGNOU website.

Our BMTC 101 Solved Assignment is independently prepared reference material intended to assist students with understanding and preparing their answers. It is not an official IGNOU publication.

Why Keep a Solved Assignment Reference?

A useful reference is more than simply a collection of answers. It can help you see how a question can be approached, what important points need attention and how the subject matter can be organised into a clear answer.

Save preparation time with organised reference material
Understand difficult questions more easily
Review important concepts before writing your answers
Improve answer organisation with a structured reference
Study conveniently whenever and wherever you need it

Product Information

Course Name	Bachelor of Science (Mathematics)
Course Code	BSCFMT
Subject Code	BMTC 101
Subject	Introduction to Probability and Statistics
Programme	BACHELOR DEGREE PROGRAMMES Courses
Language	English
Material Type	Solved Assignment – Soft Copy / PDF

Ready to Make Your BMTC 101 Assignment Preparation Easier?

Get the 2026 BMTC 101 Introduction to Probability and Statistics Solved Assignment as a convenient reference for your assignment preparation.

Call: 9199852182 / 9852900088
WhatsApp: 9199852182

IGNOU BMTC 101 2026 Solved Assignment
Get your reference copy and start preparing with confidence.

Important Note for IGNOU Students

Always check the latest assignment questions and submission instructions on the official IGNOU website before preparing and submitting your assignment. Use this solved assignment as a study and reference resource and prepare your own submission according to the applicable IGNOU requirements.

Why Choose IGNOU Academy for Your Assignments?

Getting your assignments right is an important part of your IGNOU academic journey.IGNOU Academy provides carefully prepared reference materials designed to makeassignment preparation simpler, clearer and more convenient for students.

Latest Curriculum: Materials are prepared with the current IGNOU syllabus and assignment requirements in mind.
Proper Assignment Format: Understand the structure, presentation and answer style generally expected in an IGNOU assignment.
Simple Explanations: Difficult topics are explained in clear and easy-to-understand language.
Exam Preparation: Assignment material can also be useful for revising important concepts before the Term-End Examination.
Student-Friendly Language: Clear English/Hindi content helps students understand topics without unnecessary complexity.
Trusted by IGNOU Learners: Students across India use IGNOU Academy as a convenient source of assignment and study-reference material.

These materials are provided as reference study guides. Students should understandthe concepts, follow IGNOU guidelines and prepare their own original assignmentswhere required.

How to Get Your Solved Assignment PDF

Visit IGNOU Academy:Go to www.ignouacademy.com.
Find Your Course:Search for your programme, course code and subject.
Select the Session:Choose the latest available reference material for your academic session.
Complete Your Order:Add the required material to your cart, log in or register, and complete the payment.
Access Your Material:After successful payment, access your purchased study material from your account.

Step-by-Step: Finding IGNOU Assignment Question Papers

Open the Website:Visit www.ignouacademy.com.
Open Assignment Question Papers:Select the relevant IGNOU assignment question paper section.
Filter Your Requirement:Select your course, session and medium such as English or Hindi.
Open the Paper:View or download the required question paper for your preparation.

How to Submit Your IGNOU Assignments

Prepare Neatly:Use the format and submission instructions applicable to your programme and study centre.
Complete the Front Page:Enter your Name, Enrollment Number, Programme/Course Code, Subject and Study Centre details correctly.
Offline Submission:If your study centre requires physical submission, submit the assignment as instructed and retain the acknowledgement.
Online Submission:Where online submission is permitted, follow the instructions issued by your Regional Centre or Study Centre. Keep proof of submission for your records.

Tracking Your Assignment Submission Status

After submitting your assignments, students can check whether their assignmentmarks and submission details have been updated through the applicable official IGNOU system.

Open the Official IGNOU Student Area:Visit the official IGNOU website and access the relevant student services.
Find Assignment Status:Open the assignment-status service applicable to your programme.
Enter Your Details:Provide your Enrollment Number and other requested programme details.
Check the Status:Review the available submission, evaluation and marks information.

A Quick Tip for IGNOU Students

Assignments are an important part of the IGNOU evaluation process. Preparing themcarefully, understanding the questions, following the prescribed format and submittingthem within the applicable deadline can help you stay on track academically.

Smart Study + Proper Preparation + Timely Submission = Better Academic Planning

Need Help? Contact IGNOU Academy WhatsApp: +91 9199852182 | Website: www.ignouacademy.com

IGNOU Solved Assignments Assignments Ignou Projects Project Previous Year Solved Exam Papers Notes Notes Sample Question Papers Sample Question Papers