Thread: random variable related

1) Let X be a random variable that takes values μ−a, μ, and μ+a with probabilities p, 1 − 2p, and p respectively. Show
Pr(|X − μ| >= a) = Var(X)/a^2

2) For a discrete random variable X, show that m = E(X) minimizes E[(X − m)^2]

Originally Posted by ashimb9

1) Let X be a random variable that takes values μ−a, μ, and μ+a with probabilities p, 1 − 2p, and p respectively. Show
Pr(|X − μ| >= a) = Var(X)/a^2

Since \ |x-\mu| \ge a[/tex] when and (assuming )



You should know how to calculate to complete the demonstration.

RonL

Originally Posted by CaptainBlack

Since \ |x-\mu| \ge a[/tex] when and (assuming )



You should know how to calculate to complete the demonstration.

RonL

But how can it be assumed for certain that a>0 ?

Originally Posted by ashimb9

But how can it be assumed for certain that a>0 ?

If , then it is always true that since is always positive.

Originally Posted by ashimb9

But how can it be assumed for certain that a>0 ?

You will probabbly find it as an extra condition somewhere, because the question makes little sense otherwise.

RonL