If the mean of a Poisson distribution is frac | vedclass

Name: Exam Paper Generator | JEE NEET Paper Generator | Vedclass
Brand: Vedclass
Rating: 5 (35 reviews)

Question

(C) Given that the mean of the Poisson distribution is $\lambda = \frac{1}{2}$.The probability mass function of a Poisson distribution is given by $P(

Vedclass · Accepted Answer

$1: 6$

Vedclass · Answer

(C) Given that the mean of the Poisson distribution is $\lambda = \frac{1}{2}$.The probability mass function of a Poisson distribution is given by $P(X=n) = \frac{\lambda^n e^{-\lambda}}{n!}$.We need to find the ratio $\frac{P(X=3)}{P(X=2)}$.$P(X=3) = \frac{(\frac{1}{2})^3 e^{-1/2}}{3!}$.$P(X=2) = \frac{(\frac{1}{2})^2 e^{-1/2}}{2!}$.Taking the ratio:$\frac{P(X=3)}{P(X=2)} = \frac{\frac{(\frac{1}{2})^3 e^{-1/2}}{3!}}{\frac{(\frac{1}{2})^2 e^{-1/2}}{2!}} = \frac{(\frac{1}{2})^3}{3!} 	imes \frac{2!}{(\frac{1}{2})^2}$.$= \frac{1}{2} 	imes \frac{2!}{3!} = \frac{1}{2} 	imes \frac{2}{6} = \frac{1}{2} 	imes \frac{1}{3} = \frac{1}{6}$.Thus,the ratio is $1:6$.

If the mean of a Poisson distribution is $\frac{1}{2}$,then the ratio of $P(X=3)$ to $P(X=2)$ is

Similar Questions

$A$ vertical spring with force constant $k$ is fixed on a table. $A$ ball of mass $m$ at a height $h$ above the free upper end of the spring falls vertically on the spring so that the spring is compressed by a distance $d$. The net work done in the process is

Three point charges are placed at the corners of an equilateral triangle. Assuming only electrostatic forces are acting,which of the following statements is true?

If $\alpha = \frac{5}{2! 3} + \frac{5 \cdot 7}{3! 3^2} + \frac{5 \cdot 7 \cdot 9}{4! 3^3} + \ldots$,then $\alpha^2 + 4\alpha$ is equal to

Heat energy is incident on the surface at the rate of $1000 ~J/min$. If the coefficient of absorption is $0.8$ and the coefficient of reflection is $0.1$,then the heat energy transmitted by the surface in $5$ minutes is: (in $~J$)

An unbanked curve has a radius of $60\,m$. The maximum speed at which a car can make a turn if the coefficient of static friction is $0.75$,is ...... $m/s$.

Vedclass Test Series

Exam Paper Generator

Online Exam Module