- #1

diracdelta

- 55

- 0

## Homework Statement

Random variable x is defined on interval (1,3) and it has probability mass function f(x) =A(x

^{2}+1=

a) Find PMF, g(y) for y=x

^{2}

b)Expectation of y

c)Variance of y

d)Distribution function of y.

e)most probable value of y

## The Attempt at a Solution

As far as a), i integrated from 1 to 3 f(x) and found A=3/32

So, for g(y) i inserted x=square root of y into f(x), plus due to it is parabola, it is multiplied by two. No problem there, and also, y is defined on [1,9]

c) and d) is easy, just integrate

d) Distribution function of y, how to find that?

I know that distribution function is F(X):=P(X<=x)= integral from -inf to x f(t)dt

How do i apply it on this very case?

e) Just derivative

Thanks for reading and spending time to answer me :)