Two dice are thrown simultaneously. If X denotes the number of sixes,…

Probability of six $P=\frac{1}{6}$  $\bar P=q=\frac{5}{6}$

X	0	1	2
P(X)	${^2C}_0(\frac{5}{6})^2$	${^2C}_1(\frac{1}{6})(\frac{5}{6})$	${^2C}_2(\frac{1}{6})^2$

$E(X)=∑P(xi)xi=0×(\frac{5}{6})^2+2×\frac{5}{6^2}+2×\frac{1}{6^2}$

$=\frac{10}{36}+\frac{2}{36}=\frac{12}{36}=\frac{1}{3}=E(X)$

$E(x^2)=0^2×(\frac{5}{6})^2+1^2\frac{2×5}{6^2}+4×\frac{1}{6^2}=\frac{10}{36}+\frac{4}{36}=\frac{14}{36}=E(x^2)$

$σ^2$ (variance) = $E(x^2)-E(x)^2=\frac{14}{36}-\frac{1}{9}=\frac{14-4}{36}=\frac{10}{36}$

$=\frac{5}{18}$