Final answer:
To find Pw(w), the probability of a specific value w for the random variable W, we need to find the corresponding probabilities for X and then apply the transformation function g(X) = -X. We can find Pw(w), Fw(w), and E[W] using the formulas and calculations explained in the steps.
Step-by-step explanation:
To find P(w), the probability of a specific value w for the random variable W, we need to find the corresponding probabilities for X and then apply the transformation function g(X) = -X. Let's go step by step:
a) Find Pw(w): We can find Pw(w) by finding Px(x) for each value of x and then substituting -x for each value.
b) Find Fw(w): Fw(w) is the cumulative distribution function for W. We can find it by finding the cumulative distribution function Fx(x) for each value of x and then substituting -x for each value.
c) Find E[W]: The expected value of W can be found by using the formula E[W] = ∑(w * Pw(w)) for all possible values of w.