Can someone help with these three random variable questions? 3. Let X be a rando

Question

Can someone help with these three random variable questions?

3. Let X be a random variable. Prove that if E(X2-E(X)], then Pr(X = E(X)) = 1. 4. Suppose a share of Microsoft is worth 400 today. Suppose that on any given day, the value goes up 4 with probability 0.2, and down 3 otherwise, independent of all else. Express the value V of a share of Microsoft 9 days from now as a function of an appropriate random variable 5. Suppose X is a random variable such that E(X) = 0 and Var(X)-1. If Y rX + s for r > 0, and E(Y) = 5, Var(Y) = 9, compute r and s.

Explanation / Answer

Question 3:

The variance of the given distribution is computed as:

Var(X) = E(X2) - (E(X))2

But as we are given that E(X2 ) = (E(X))2, therefore, we get:

Var(X) = E(X2) - (E(X))2= 0

Now as the variance of the given distribution is 0, therefore, all the terms of the given distribution must be the same and hence they would be equal to the mean value that is P(X = E(X) ) = 1, Hence proved.

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