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(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

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$2$

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(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.

$X = x_i$	$0$	$1$	$2$	$3$	$4$
$P(X = x_i)$	$0.4$	$0.3$	$0.1$	$0.1$	$0.1$

No. of Pizzas $(x_i)$	$5$	$6$	$7$	$8$	$9$	$10$
Probability $(P_i)$	$0.07$	$0.2$	$0.3$	$0.3$	$0.07$	$0.06$

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

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