AP EAMCET2013MathematicsProbability
If X is a poisson variate P(X=1)=2 P(X=2) , then P(X=3) is equal to
Options
- Ae⁻¹ 6
- Be⁻² 2
- Ce⁻¹ 2
- De⁻¹ 3
Correct answer
A. e⁻¹ 6
Step-by-step solution
In poission distribution gathered P(X=x)= ^x e^ - x ! P(X=1)= e^ - 1 ! = e^ - P(X=2)= ^2 e^ - 2 ! = ^2 e^ - 2 P(X=1)=2 P(x=2) e^ - =2 ^2 e^ - 2 ( -1)=0 gathered aligned & 0 & =1 aligned Hence, P(X=3)= (1)^3 e⁻¹ 3 ! = e⁻¹ 6 ( =1)