Q1: the random variable X is exponentially distributed with mean lamda. let Y be the integer part of X. That is, if X [n, n + 1), then Y=n. Find the pgf of 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 defined as the minimum of X1 and X2: Find the probability generating

function of Y

Q3: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 of i=1 to n for (xi-mean)^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.

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