If the p.m.f. of a r.v. X is then, the standard deviation of X is (given p+q=1 )

Step-by-step solution

(B) array |c|c|c|c| x _ i & p _ i & p _ i x _ i & p _ i x _ i ² 0 & q ² & 0 & 0 1 & 2 pq & 2 pq & 2 pq 2 & p ² & 2 p ² & 4 p ² Total & & 2 pq +2 p ² & 2 pq +4 p ² array Mean ( )= E ( x )= p _ i x _ i =2 p ( p + q )=2 p [ p + q =1 , given ] Variance ( _ x ² )= p _ i x _ i ²- ²=2 pq +4 p ²-4 p ²=2 pq Standard deviation ( _ x )= 2 pq