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Okay - here's the question.
Let X be a random variable with probability mass function given by p(-4) = p(4) = 1/16 and p(2) = p(-2) = 7/16. Let Y = aX+b for a certain a and b.
Part A asks: For what values of a and b does Y take values in {0,1,2,3,4}?
Now, I solved this part and got a = +/- .5 and b = 2.
However, my trouble lies in figuring out the answer to this question:
Compute the probability mass function of Y for these choices of a and b.
It doesn't actually matter whether a is 0.5 or -0.5, the probability mass function will be the same either way.
You just substitute the probability function for X into the equation to get the function for Y.
For example, for X, p(-4)=1/16.
In this case, Y = -4*0.5 + 2 = 0. Therefore, for Y, p(0)=1/16.
Similar reasoning for the rest gives that p(1) = p(3) = 7/16 and p(4) = 1/16.
Why did the vector cross the road?
It wanted to be normal.
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