Question

Consider a Poisson distribution for the tossing of a biased coin. The mean for this distribution is $\mu$. The standard deviation for this distribution is given by ______.

• (A) $\sqrt{\mu }$
• (B) ${\mu }^2$
• (C) $\mu$
• (D) $\frac{1}{\mu }$

Answer 1

The Correct Option is A

Explanation:
Poisson distribution formula,$P(x)=\frac{e^{-\lambda }{\lambda }^x}{x!}$where $\lambda =$ mean value of occurrence within an interval $P(x)=$ probability of $x$ occurrence within an interval For Poisson Distribution we haveMean $=$ Variance $=$ (Standard Deviation)${}^2$$\therefore$ Standard Deviation $=\sqrt{\text{ Mean }}=\sqrt{\mu }$Hence, the correct option is (A).