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## Homework Statement

Let X be a discrete random variable with probability mass function p given by:

a ...| -1 .| 0 ..| 1 ..| 2

-----+-----+-----+-----+---

p(a) | 1/4 | 1/8 | 1/8 | 1/2

and p(a) = 0 for all other a.

a.) Let random variable Y be defined by Y = X^2. Calculate the probability mass function of Y.

b.) Calculate the distribution functions for X and Y in a = 1, a = 3/4, a = pi - 3

## Homework Equations

n/a

## The Attempt at a Solution

a.) I know that if X = 2, Y = 4. And if X = 0, Y = 0, so

Py(4) = Px(2) = 1/2 and

Py(0) = Px(0) = 1/8

But what about -1 and 1? Does this mean that Py(1) = Px(-1) + Px(1)?

b.) Since we're only dealing with whole numbers, is it true that the probability distribution function for X and Y on a = 1, a = 3/4, a = pi - 3 is equal to PX(1) + PX(0) and PY(1) + PY(0) respectively?