For a mesokurtic distribution with standard deviation 5, find fourth central moment m4.
In a mesokurtic distribution, the kurtosis value is approximately 3, which is the same as the kurtosis of a normal distribution. The kurtosis _____ ____ _____ __________ ____ __________ _______.
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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 =2 against the alternative hypothesis that is
=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.
6 observations on (X ,Y) yielded the following data:
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 ?
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
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.
You may like to use the following values:
P(Z>1.25) = 0.1056
P(Z< -0.525) = 0.3
If X is a random variable such that E(X)=3 and E(X2) = 13, determine a lower bound for P(-2< X <8).
एक पासे को 60 बार फेंकने से निम्नलिखित परिणाम प्राप्त होते हैं:
5% सार्थकता स्तर पर परीक्षण कीजिए कि पासा अनभिनत है। दिया गया है कि 5, 6 और 7 स्वातंत्र्य कोटि के लिए %' के मान क्रमशः 11.070, 15.592 और 14.067 हैं।
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.
Let X be a gamma variable with parameters and
, having E(X) = 6 and Var (X)=3. 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.