A random variable x has a following probability distribution.
x: 0 1 2 3
P(X=x): 1/6 1/2 1/5 2/15
How to calculate E(1/(X+1))?
Let Y=1/(X+1) then
y:1, 1/2, 1/3, 1/4
P(Y=y):1/6, 1/2, 1/5, 2/15
E(Y)=1*1/6+1/2*1/2+1/3*1/5+1/4*2/15
x: 0 1 2 3
P(X=x): 1/6 1/2 1/5 2/15
How to calculate E(1/(X+1))?
y:1, 1/2, 1/3, 1/4
P(Y=y):1/6, 1/2, 1/5, 2/15
E(Y)=1*1/6+1/2*1/2+1/3*1/5+1/4*2/15