12,

13.

14.

15.

16.

11,

18,
19.
20.

21.
22,

28.

24.

25.

26,

A random variable X has mean 3 and variance 2. Use Tchebychev's inequality to obtain an
upper bound for रन & 2.

If x is a random variable distributed as N (0,1), show that ¥ = X* has gamma distribution.

Let X has the density f(x)=1,0
In the analysis of data of randomized block design with 5 blocks and 4 treatments, what is
the degrees of freedom for the error variations?

What are the basic assumptions of ANOVA?

The two regression lines are X +2¥ =0 and 2X +3Y =8. Variance of Y =4 . What is the
value of variance of X7

Differentiate between estimator and estimate.
What are the properties of distribution function of a random variable?
Write down the characteristic function of a normal distribution.

If the first four raw moments of & random variable X are 1,2.3 and 4 respectively, find the
first four central moments.

What is the relationship between t—distribution and F - distribution?

For the sequence of random variables {X,} with ‏متام‎ நர்‌ | ‏م ئا وی‎ அ - Test whether

1

weak law of large numbers holds for [2 ‏۔.‎

How will you test the significance of correlation coefficient r?

Find the coefficient, of skewness if the difference between third and 5:91 quartiles is 8, sum of
these quartiles is 22 and the median is 10.5.

Variance (r)= 25 and mean (x)= 308, find the coefficient of variation.

2 "66/2015