Let the random variable X have a pmf px 13 x 123 zero else

Let the random variable X have a p.m.f. p(x) = 1/3, x = 1,2,3, zero elsewhere. Find the p.m.f. of Y = 2X + 1. Let X be a random variable with the expected value of X equal to one hundred and sigma2 equal to fifteen. What are... E (X2 ) .E (-X) E ( 3X + 10 ) Standard deviation of -X ?

Solution

p(x) = 1/3, x = 1,2,3

Y = 2x+1

y can take values as 3, 5, 7

Prob (y) = 1/3 for y = 3,5,7

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b) E(x) = 100

sigma^2 = 15

E(X^2)-100^2 = sigma^2

So

i) E(x^2) = 10015

ii) E(3x+10) = 3E(X)+10

= 310

iii) E(_x) = -E(X) = -100

iv. Var (-x) = Var (X) = 15

std dev of -x = rt 15