Question

If in a poisson frequency distribution, the frequency of $3$ successes is $\frac{2}{3}$ times the frequency of $4$ successes, the mean of the distribution is

• A. $\frac{2}{3}$
• B. $\frac{1}{3}$
• C. $6$
• D. $\sqrt{6}$

Answer 1

The correct option is C $6$

According to question
$P(X=3;\mu )=\frac{2}{3}P(X=4;\mu )$
$\frac{e^{-\mu }{\mu }^3}{3!}=\frac{2}{3}\frac{e^{-\mu }{\mu }^4}{4!}$
=> $\frac{e^{-\mu }{\mu }^3}{6}=\frac{e^{-\mu }{\mu }^4}{36}$
=> $e^{-\mu }{\mu }^3[\frac{1}{6}-\frac{\mu }{36}]$
=> $\mu =0or\mu =\frac{36}{6}=6$