The probability function of a random variable is defined as : | $X = x$ | $-1$ | $-2$ | $0$ | $1$ | $2$ | | --- | --- | --- | --- | --- | --- | | $P(x)$ | $k$ | $2k$ | $3k$ | $4k$ | $5k$ | Then value of k is : (a) $\frac{1}{15}$ (b) Zero (c) One (d) $\frac{1}{4}$

The probability function of a random variable is d – Class 12 Business Mathematics Statistics

Question 39 of 41

The probability function of a random variable is defined as :

$X = x$	$-1$	$-2$	$0$	$1$	$2$
$P(x)$	$k$	$2k$	$3k$	$4k$	$5k$

Then value of k is :

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The total probability must equal $1$ : $15k=1\Rightarrow k=\tfrac{1}{15}$ .

For $P(x)$ to be a valid probability mass function, all probabilities are non-negative and their sum is $1$ :

$\sum P(x) = k + 2k + 3k + 4k + 5k = 15k.$

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