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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:

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.

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