The range of a random variable X is {1, 2, 3, | vedclass

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(C) We know that for any probability distribution,the sum of all probabilities must be equal to $1$. Given $P(X=x) = \frac{c^x}{x!}$ for $x = 1, 2, 3,

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$\ln(2)$

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(C) We know that for any probability distribution,the sum of all probabilities must be equal to $1$. Given $P(X=x) = \frac{c^x}{x!}$ for $x = 1, 2, 3, \ldots$. Therefore,$\sum_{x=1}^{\infty} P(X=x) = 1$. Substituting the given expression: $\sum_{x=1}^{\infty} \frac{c^x}{x!} = 1$. We know the Taylor series expansion for the exponential function is $e^c = \sum_{x=0}^{\infty} \frac{c^x}{x!} = 1 + \frac{c}{1!} + \frac{c^2}{2!} + \frac{c^3}{3!} + \ldots$. Thus,$\sum_{x=1}^{\infty} \frac{c^x}{x!} = e^c - 1$. Setting this equal to $1$: $e^c - 1 = 1$. $e^c = 2$. Taking the natural logarithm on both sides: $c = \ln(2)$.

$X$	$0$	$1$	$2$
$P(X)$	$0.4$	$0.4$	$0.2$

The range of a random variable $X$ is $\{1, 2, 3, \ldots\}$ and $P(X=x) = \frac{c^x}{x!}$ for $x = 1, 2, 3, \ldots$. Then the value of $c$ is

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