Let X be a gamma variable with parameters and
, having
and
. Find
and
. 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?
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मान लीजिए कि r.v. X का प्रायिकता घनत्व फलन निम्नलिखित है :
और यदि और
हो, तो Cov(u,v) ज्ञात कीजिए। u और v के स्वांतन्त्र्य की भी जाँच कीजिए।
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.
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.
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 बच्चों की I.Q. होगी।
आप निम्नलिखित मानों का प्रयोग कर सकते हैं :
(X, Y ) पर किए गए 6 प्रेक्षणों से प्राप्त आँकड़े निम्नलिखित हैं :
$
i) X और Y के बीच सहसंबंध-गुणांक ज्ञात कीजिए।
ii) दिया गया है , तब Y का प्रागुक्त मान क्या होगा?
iii) दिया गया है , तो X प्रागुक्त मान क्या होगा?
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)
Consider the joint probability density function$
Are both x and y regressions linear? Give reasons for your answer.
Let X be a gamma variable with parameters and
, having
and
. Find
and
. 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?