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 k is equal to : (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 20 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 k is equal to :

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$k = \dfrac{1}{15}$ .

For a discrete random variable, the total probability must equal $1$ :

$\sum P(x) = 1.$

Adding the given probabilities:

$k + 2k + 3k + 4k + 5k = 15k.$

Set the sum equal to $1$ :

$15k = 1 \;\Rightarrow\; k = \frac{1}{15}.$ …