Find the variance and std deviation of the r.v.x whose probability distribution is given below:
$x$ 0 1 2 3
$P (X = x)$ $\frac{1}{8}$ $\frac{3}{8}$ $\frac{3}{8}$ $\frac{1}{8}$

Open in App

Solution

variance $= σ^{2} = \sum {x_{i}}^{2} p_{i}$
$= u^{2} \times \frac{1}{8} + 1^{2} \times \frac{3}{8} + 2^{2} \times \frac{3}{8} + 3^{2} \times \frac{1}{8}$
$= \frac{3}{8} + \frac{12}{8} + \frac{9}{8}$
$σ^{2} = \frac{24}{8}$
Vairance $= σ^{2} = 3$
Standard derivation $= \sqrt{3}$

Suggest Corrections

Similar questions

X

$x$	$0$	$1$	$2$	$3$
$P (X = x)$	$\frac{1}{8}$	$\frac{3}{8}$	$\frac{3}{8}$	$\frac{1}{8}$

x

X = x : 0123

p (X = x) : \frac{1}{3} \frac{1}{2} 0 \frac{1}{6}

The probability distribution of the random variable X is given below

X: 0 1 2 3

$P (X) : k \frac{k}{2} \frac{k}{4} \frac{k}{8}$ Then the value of k is

\frac{4}{3}

\frac{8}{9}

P (x \geq 1)

$x_{i}$	$4$	$8$	$11$	$17$	$20$	$24$	$32$
$f_{i}$	$3$	$5$	$9$	$5$	$4$	$3$	$1$

Join BYJU'S Learning Program