If a random variable X follows the Poisson di | vedclass

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

Question

(C) For a Poisson distribution, the variance is equal to the parameter $\lambda$. Given that the variance is $3$, we have $\lambda = 3$. The probabili

Vedclass · Accepted Answer

$2$

Vedclass · Answer

(C) For a Poisson distribution, the variance is equal to the parameter $\lambda$. Given that the variance is $3$, we have $\lambda = 3$. The probability mass function is given by $P(X=r) = \frac{e^{-\lambda} \lambda^r}{r!}$. For a Poisson distribution, the probability $P(X=r)$ is maximum when $r = \lfloor \lambda \rfloor$ if $\lambda$ is not an integer, and it takes two maximum values at $r = \lambda$ and $r = \lambda - 1$ if $\lambda$ is an integer. Here, $\lambda = 3$, which is an integer. Therefore, $P(X=r)$ is maximum at $r = 3$ and $r = 3 - 1 = 2$. Comparing this with the given options, $r=2$ and $r=3$ are both valid, but since $r=2$ is provided in the options, it is a correct value.

$X = x$	$-1$	$0$	$1$	$2$
$F(X = x)$	$0.3$	$0.7$	$0.8$	$1$

If a random variable $X$ follows the Poisson distribution with variance $3$, then $P(X=r)$ is maximum, when $r=$

Similar Questions

The cumulative distribution function $F(x)$ of a discrete random variable $X$ is given by the following table:
$X = x$ $-1$ $0$ $1$ $2$
$F(X = x)$ $0.3$ $0.7$ $0.8$ $1$

Then $E(X^2) = $

Find the mean number of heads in three tosses of a fair coin.

If the probability of a bad reaction from a vaccination is $0.01$, then the probability that exactly two out of $300$ people will get a bad reaction is

If $X$ is a random variable with probability distribution $P(X=k) = \frac{(2k+3)c}{3^k}$, $k=0, 1, 2, \ldots, \infty$, then $P(X=3) =$

Two numbers are selected at random (without replacement) from the first six positive integers. Let $X$ denote the larger of the two numbers obtained. Find $E(X)$.

Vedclass Test Series

Exam Paper Generator

Online Exam Module