# Math Help - probability theory

1. ## probability theory

Hi guys!

Can you help me with this:

Let Y be a random variable taking values 0 and 1 with probability 0.5
each. Find expected values of random variable Z = X·Y

2. ## Re: probability theory

Hey nstockholm.

What is X? Is it a constant or random variable? What is its distribution (if its a random variable)?

3. ## Re: probability theory

here is the whole problem , I solved 2a but 2b I don't know

4. ## Re: probability theory

here is problem

5. ## Re: probability theory

If X and Y are independent then $E[XY]=E[X]\times E[Y]$

6. ## Re: probability theory

ok? but what happen then ?

7. ## Re: probability theory

Hi nstockholm,

I think the issue might be this: The problem asks you to find the expected values of Z and their probabilities, not the expected value of Z. This is probably a poor choice of words. It would be better to call them possible values or something like that.

It is clear that the possible values of Z are the same as those of X, since multiplying with Y means multiplying by either 0 or 1. Can you find the new probabilities?

8. ## Re: probability theory

Form the joint distribution using independence P(A = a, B = b) = P(A = a)P(B = b) and calculate the expectation (you can also use Shakarri's hint above which will give you the exact same answer).