q1:The random variable X is exponentially distributed with mean : Let Y be the integer part of

X: That is, if X 2 [n; n + 1) ; then Y = n: Find the pgf of Y and hence E (Y ) ;E fY (Y ô€€€ 1)g and var Y

q2

The random variables X1 and X2 are i.i.d, with probability functions

f (x) =

(1 - p)^(x-1) p ; x = 1, 2....

0 ; otherwise.

The random variable Y is deFINned as the minimum of X1 and X2: Find the probability generating

function of Y

q3:Question 6

The random variables X1.....Xn are i.i.d. N(0; 1) random variables. The sample variance is

deFIned as s^2= 1/n-1*(sum from i=1 to n for (Xi-X)^2)

In STAT271 we shall show that (n - 1)S^2 has the x^2 distribution with degrees of freedom

n - 1. For the special case where n = 2, show this directly. You will need to specify every rule

you have used.

X: That is, if X 2 [n; n + 1) ; then Y = n: Find the pgf of Y and hence E (Y ) ;E fY (Y ô€€€ 1)g and var Y

q2

The random variables X1 and X2 are i.i.d, with probability functions

f (x) =

(1 - p)^(x-1) p ; x = 1, 2....

0 ; otherwise.

The random variable Y is deFINned as the minimum of X1 and X2: Find the probability generating

function of Y

q3:Question 6

The random variables X1.....Xn are i.i.d. N(0; 1) random variables. The sample variance is

deFIned as s^2= 1/n-1*(sum from i=1 to n for (Xi-X)^2)

In STAT271 we shall show that (n - 1)S^2 has the x^2 distribution with degrees of freedom

n - 1. For the special case where n = 2, show this directly. You will need to specify every rule

you have used.