Q54 / 160 · AP EAMCET 2003 · Mathematics

For a poisson variate $X$, if $P(X=2)=3 P(X=3)$, then the mean of $X$ is :

  • Correct answer
    A
    1
  • B
    $\frac{1}{2}$
  • C
    $\frac{1}{2}$
  • D
    $\frac{1}{4}$

Solution

We know that, $P(X=k)=\frac{\lambda^k e^\lambda}{k !}$ Since, $P(X=2)=3 P(X=3)$ $\Rightarrow \quad \frac{\lambda^2 e^\lambda}{2 !}=3 \cdot \frac{\lambda^3 e^\lambda}{3 !} \Rightarrow \lambda=1$ $\therefore$ Mean of poisson distribution $=\lambda$ $=1$

Hence, the correct answer is option: 'A'.

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