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।
_______ ____ __________ ___ ________ ______ ___ _______ ___ ______.
_____ _______ ________ ________ _________ _____ _______ ___ _______ _________ ______.
__________ ____ ____ _________ ____ ________ ________ ______.
_________ __________ _______ _________ ________ ____.
__________ _______ ______ ____ ___ ______ ________ ____ ____.
________ ____ _______ ____ ________ _______ ___ ____ ____ ______ _________ _________.
_______ _______ _______ ______ _____.
_____ ___ _______ _______ ________ _______ ________ _______.
__________ ______ ___ __________ ____ ____ __________ ________.
________ ____ ___ __________ ___ ________ ______ ________ _______ ______.
_________ ___ _______ ________ ______ _____ ______.
_______ _______ _____ __________ ___.
_______ _______ ___ _____ _________ ________ _______ ________ _______ _____.
_____ _________ ________ ____ ________ __________ _____ ________ _________ ________ ________.
_________ ___ __________ ___ ________ ________ _______ ___ ________ _________ _________.
________ ___ _________ ____ _______ ____.
_______ ___ _______ ___ ________ __________ ____ _____ _______.
___ ____ ___ ________ __________ __________ __________ ______ _________ ____ ______ ________.
__________ ____ _______ _______ ___ _____ ______ __________ _______ ________ ______ ____.
__________ ___ ______ _______ _______ ______ _____ ___ _____ ________ __________ _________.
__________.
- Solved Assignments
- Study Notes
- Guess Papers
- Question Papers
✓ Unlock up to 60% of the answer
✓ No payment required
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.
. Consider the joint probability density function
Are both x and y regressions linear? Give reasons for your answer.
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
is a probability density function.
iv) For a normal distribution with mean and variance
, the hypotheses
and
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.
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 level of significance. Given that at 5, 6 and 7 d.f. the value of
are 11.070, 15.592 and 14.067 respectively.
The mean and standard deviation of a variable x are m and respectively. Obtain the mean and standard deviation of
, where a, b and c are constants.
b) If X is a random variable such that
and
, determine a lower bound for P(-2 < X < 8).
) 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।
) Let X1 be an observation from an exponential distribution with the p.d.f.
Test the null hypothesis that the mean of the distribution is against the alternative hypothesis that is
. 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.