If X is a random variable with probability mass function P (x)=k … - Vidyadip

MCQ

If $X$ is a random variable with probability mass function
$P (x)=k x \quad, \quad$ for $x=1,2,3$
$=0$. otherwise then $k=\ldots$

A
$\frac{1}{5}$
B
$\frac{1}{4}$
✓
$\frac{1}{6}$
D
$\frac{2}{3}$

✓

Answer

Correct option: C.

$\frac{1}{6}$

$x$	$1$	$2$	$3$
$P(x)$	$k$	$2k$	$3k$

Since, the function is a $\text{p.m.f.}$
$\therefore ∑P(x_i) = 1$
$\therefore k + 2k + 3k = 1$
$\therefore k = 1/6$

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