Question

For a discrete random variable y the probability distribution is f(y)={(5-y)/10,y=1,2,3,4

{0,elsewhere

Calculate E(y) and var(y)

Answer 1

The random variable Y takes the following values:

1, with P(Y=1)=(5-1)/10=0.4

2, with P(Y=2)=(5-2)/10=0.3

3, with P(Y=3)=(5-3)/10=0.2

4, with P(Y=4)=(5-4)/10=0.1

Therefore

$E(Y)=1\cdot 0.4 + 2 \cdot 0.3 + 3 \cdot 0.2+4\cdot 0.1= 2$

$E(Y^2)=1^2\cdot 0.4 + 2^2 \cdot 0.3 + 3^2 \cdot 0.2+4^2\cdot 0.1=5$

$Var(Y)=E(Y^2)-E(Y)^2=5-2^2=1$