이항분포 기댓값

$P ( X = r ) = _{n} C _{r} p ^{r} q ^{n-r} ( \text{단} , q = 1 - p )$이므로 $\displaystyle P ( X = 4 ) = \frac{1}{3} P ( X = 5 )$ $\displaystyle \therefore _{10} C _{4} p ^{4} q ^{6} = {\frac{1}{3}} \times _{10} C _{5} p ^{5} q ^{5}$을 정리하면 $\displaystyle p = \frac{5}{7}$ $\displaystyle \therefore B ( 10 , \frac{5}{7} )$에서 $\displaystyle E ( 7 X ) = 7 E ( X ) = 7 \times \frac{50}{7} = 50$