Question

x	0	1	2	3	4
P(X = x)	0.45	0.35	0.15	0.03	0.02

Find the variance of X.                                  

Answer 1

xi	pi	pixi	pixi2
0	0.45	0	0
1	0.35	0.35	0.35
2	0.15	0.30	0.60
3	0.03	0.09	0.27
4	0.02	0.08	0.32
	Total	0.82	1.54

E(X) = μ = ∑ p_ix_i = 0.82

To find Var (X) use the formula : 

`"Var"("X") = sum "p"_"i""x"_"i"^2 - µ^2`

= `1.54 - (0.82)^2`

= 1.54 -0.6724

= 0.8676

Thus , Var (X) = 0.8676