Question

A random variable X takes the values 0,1,2,3,..., with prbability PX(=x)=k(x+1)( 1 5 )x, where k is a constant, then P(X=0) is. A. 7 25 B. 16 25 C. 18 25 D. 19 25 Select the correct answer from above options

Answer 1

Correct Answer - B The Probability distribution of X is P(X=x)=k(x+1)( 1 5 )x,x=0,1,2,3,.... ∴ ∞ ∑ x=0 P(X=x)=1 ⇒k ∞ ∑ x=0 (x+1)( 1 5 )x=1 ⇒k{1+2×( 1 5 )+3×( 1 5 )2+4×( 1 5 )3+.....}=1 ⇒k{ 1 1- 1 5 + 1× 1 5 (1- 1 5 )2 }=1[∵a+(a+d)r+(a+2d)r2+.......= a 1-r + dr (1-r)2 ] ⇒k× 25 16 =1⇒k= 16 25 .