Let X be a random variable such that PX 0 1 and Mu EX exi

Let X be a random variable such that P(X > 0) = 1 and Mu = E(X) exists and is finite. Show that(X > or = to 2 Mu )

Solution

as you can see P(x>0)= 1 so we just have 1 variable x=0 because the sum of probabilities is 1

X> 2 miu can be any number finite but miu can only be the mean that is 1/2

so 2miu = 2* (1/2) = 1

X > 2miu will be lower than 1/2