Question

If X is a Poisson variate such that P (X = 2) = 9P (X = 4) + 90 P (X = 6), then Var (X) is given by -

• A. ½
• B. 1
• C. 3/2
• D. 2

Answer 1

Answer: (B)

1

Answer 2

Suppose X ~ P(l)

P(X = 2) = 9P (X = 4) + 90 P (X = 6)

Ž $\frac { \lambda ^ { 2 } } { 2 ! }$ e^–l = 9 $\frac { \lambda ^ { 4 } } { 4 ! }$e^–l + 90 $\frac { \lambda ^ { 6 } } { 6 ! }$ e^–l Ž l⁴ + 3l² – 4 = 0

Ž (l² + 4) (l² – 1) = 0 As l² + 4 > 0, l² = 1 Ž l = 1

Var (X) = l = 1