If X is a Poisson variate such that P(X=2)=P( | vedclass

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

Question

(A) $X$ is a Poisson variate. Given $P(X=2) = P(X=3)$. Using the formula $P(X=r) = \frac{e^{-\lambda} \cdot \lambda^r}{r!}$,we have: $\frac{e^{-\lambd

Vedclass · Accepted Answer

$\left(\frac{3}{2}\right)^3$

Vedclass · Answer

(A) $X$ is a Poisson variate. Given $P(X=2) = P(X=3)$. Using the formula $P(X=r) = \frac{e^{-\lambda} \cdot \lambda^r}{r!}$,we have: $\frac{e^{-\lambda} \cdot \lambda^2}{2!} = \frac{e^{-\lambda} \cdot \lambda^3}{3!}$ $\Rightarrow \frac{\lambda^2}{2} = \frac{\lambda^3}{6}$ $\Rightarrow \lambda = \frac{6}{2} = 3$. Now,we calculate $P(X=4)$: $P(X=4) = \frac{e^{-\lambda} \cdot \lambda^4}{4!} = \frac{e^{-3} \cdot 3^4}{4!}$. Finally,we find $e^3 P(X=4)$: $e^3 P(X=4) = e^3 \cdot \frac{e^{-3} \cdot 3^4}{4!} = \frac{3^4}{4!} = \frac{81}{24} = \frac{27}{8} = \left(\frac{3}{2}\right)^3$.

If $X$ is a Poisson variate such that $P(X=2)=P(X=3)$,then $e^3 P(X=4)$ is

Similar Questions

If $P(X=x)=k\left(\frac{3}{8}\right)^{X}, x=1,2,3, \ldots$ is the probability distribution function of a discrete random variable $X$,then $k=$

If $X$ is a Poisson variable such that $3 P(X=4)=\frac{1}{2} P(X=2)+P(X=0)$,then the mean of $X$ is

An observer counts $240$ vehicles per hour at a specific location on a highway. Assuming that the arrival of vehicles at the location follows a Poisson distribution, the probability that more than two vehicles arrive over a $30 \text{ sec}$ time interval is

Suppose that two cards are drawn at random from a deck of cards. Let $X$ be the number of aces obtained. Then the value of $E(X)$ is

$A$ random variable $X$ takes the values $0, 1, 2$. Its mean is $1.2$. If $P(X=0)=0.3$,then $P(X=1)=$

Vedclass Test Series

Exam Paper Generator

Online Exam Module