Question

For the random variable X with the given probability mass function as below, find the mean and variance.

`f(x) = {{:(1/10, x = 2","  5),(1/5, x = 0","  1","  3","  4):}`

Answer 1

Probability mass function

x	0	1	2	3	4	5
F(x)	`1/5`	`1/5`	`1/10`	`1/5`	`1/5`	`1/10

Mean: `mu = "E"("X")`

= `sum x f(x)`

= `0 xx 1/5 + 1 xx 1/5 + 2 xx 1/10 + 3 xx 1/5 + 4 xx 1/5 + 5 xx 1/10`

= `0 + 1/5 + 2/10 + 3/5 + 4/5 + 5/10`

= `23/10`

= 2.3

Variance: `"E"("X"^2)`

= `sum x^2 f(x)`

= `0^2 xx 1/5 + 1^2 xx 1/5 + 2^2 xx 1/10 + 3^2 xx 1/5 + 4^2 xx 1/5 + 5^2 xx 1/10`

= `0 + 1/5 + 4/10 + 9/5 + 16/5 + 25/10`

= `81/10`

= 8.1

Var(X)= E(X²) – [E(X)]²

= 8.1 – (2.3)²

= 8.1 – 5.29

= 2.81