Question

Four fair coins are tossed once. Find the probability mass function, mean and variance for a number of heads that occurred

Answer 1

Let X be the random variable that denotes the number of heads when four coins are tossed once.

X ={0, 1, 2, 3}

n(S) = 16

Values of random variable	0	1	2	3	4	Total
Number of elements in inverse image	1	4	6	4	1	16

Probability mass function

x	0	1	2	3	4
F(x)	`1/16`	`4/16`	`6/16`	`4/16`	`1/16`

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

= `0 xx 1/16 + 1 xx 4/16 + 2 xx 6/6 + 3 xx 4/16 + 4 xx 1/16`

= `32/16`

= 2

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

= `0^2 xx 1/16 + 1^2 xx 4/16 + 2^2 xx 6/16 + 3^2 xx 4/16 + 4^2 xx 1/16`

= `0 + 4/16 + 24/16 + 36/16 + 16/16`

= `80/16`

= 5

Var(X) = E(X²) – [E(X)]²

= 5 – 4

= 1