A random variable X has the following probability distribution X … - Vidyadip

MCQ

A random variable $X$ has the following probability distribution

$X$	$0$	$1$	$2$	$3$	$4$
$P(X)$	$k$	$2$	$4k$	$6k$	$64$

The value of $P (1< X <4 \mid X \leq 2)$ is equal to

✓
$\frac{4}{7}$
B
$\frac{2}{3}$
C
$\frac{3}{7}$
D
$\frac{4}{5}$

✓

Answer

Correct option: A.

$\frac{4}{7}$

a
$P \left(\frac{1< x <4}{ x \leq 2}\right)=\frac{ P (1< x <4 \cap x \leq 2)}{ P ( x \leq 2)}$

$=\frac{ P (1< x \leq 2)}{ P ( x \leq 2)}=\frac{ P ( x =2)}{ P ( x \leq 2)}$

$=\frac{4 k }{ k +2 k +4 k }$

$=\frac{4}{7}$

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