# Thread: PMF of random variable

1. ## PMF of random variable

Ok so I have a PMF of X:

$\displaystyle P_X(x) = x^2/a$ for $\displaystyle x = -3, -2, -1, 0, 1, 2, 3,$
$\displaystyle 0, otherwise.$

(sorry - I don't really know how to write the PMFs on here but that was my best attempt)

we had to work out a which I have as 28, and then $\displaystyle E[X]$ which I got to be 0.

However now I have to work out the PMF of Y if $\displaystyle Y = (X - E[X])^2$

I really don't know how to approach this! I know it's something really simple but I can't think how I would do this!

I know that as the expectation is 0, $\displaystyle Y = X^2$
but from there I am unsure of how to get the PMF.

2. ## Re: PMF of random variable

Re-looking at this I think that $\displaystyle a = 7x^2$
but assurance would be lovely!!!
Not that anyone is actually looking at this but yeah....

3. ## Re: PMF of random variable

Originally Posted by Natalie11391
Re-looking at this I think that $\displaystyle a = 7x^2$
but assurance would be lovely!!!
Not that anyone is actually looking at this but yeah....
You have to solve $\displaystyle \frac{9}{a} + \frac{4}{a} + \frac{1}{a} + 0 + \frac{1}{a} + \frac{4}{a} + \frac{9}{a} = 1$ for a.

So your original answer of a = 28 is correct. I don't know why you have said a = 7x^2.

4. ## Re: PMF of random variable

Originally Posted by Natalie11391
Ok so I have a PMF of X:

$\displaystyle P_X(x) = x^2/a$ for $\displaystyle x = -3, -2, -1, 0, 1, 2, 3,$
$\displaystyle 0, otherwise.$

(sorry - I don't really know how to write the PMFs on here but that was my best attempt)

we had to work out a which I have as 28, and then $\displaystyle E[X]$ which I got to be 0.

However now I have to work out the PMF of Y if $\displaystyle Y = (X - E[X])^2$

I really don't know how to approach this! I know it's something really simple but I can't think how I would do this!

I know that as the expectation is 0, $\displaystyle Y = X^2$
but from there I am unsure of how to get the PMF.
The sample space for $\displaystyle Y$ is $\displaystyle \{0,1,4,9\}$, now use the PMF of $\displaystyle X$ to evaluate the probability that $\displaystyle Y$ takes each of these values.

CB

5. ## Re: PMF of random variable

I was just about to delete this because I eventually figured it out but thank you for helping anyway

I thought it would be $\displaystyle 7x^2$ because a friend told me that he got that and that 28 was wrong but yeah, it turns out I WAS right originally!

Thanks guys

6. ## Re: PMF of random variable

Originally Posted by Natalie11391
I was just about to delete this because I eventually figured it out but thank you for helping anyway

[snip]
Memo to all members: Don't delete posts. See the rules.

7. ## Re: PMF of random variable

oo ok!! Well I wasn't going to seeing as it now has replies but if something doesn't have any replies and it's been up for a while, can you still not delete it?