The probability distribution of a random variable $X$ is given below
$X = x$ $- 1.5$ $- 0.5$ $0.5$ $1.5$ $2.5$
$P [X = X]$ $0.05$ $0.2$ $0.15$ $0.25$ $0.35$
The variance of $X$ is

1.6

No worries! We‘ve got your back. Try BYJU‘S free classes today!

0.24

No worries! We‘ve got your back. Try BYJU‘S free classes today!

0.84

Right on! Give the BNAT exam to get a 100% scholarship for BYJUS courses

0.75

No worries! We‘ve got your back. Try BYJU‘S free classes today!

Open in App

Solution

The correct option is C $0.84$
Now, $V a r (X) = (x - μ)^{2} P (X - x)$

Now, we have

$μ = 0 \times 1 + 0.4 \times 1 + 0.3 \times 2 + 3 \times 0.2 + 4 \times 0 = 1.6$
Thus, we have $V a r (X) = (0 - 1.6)^{2} \times 0.2 + (1 - 1.6)^{2} \times 0.4 + (2 - 1.6)^{2} \times 0.3 + (3 - 1.6)^{2} \times 0.2 + (4 - 1.6)^{2} \times 0$

Thus, $V a r (X) = 0.256 + 0.144 + 0.048 + 0.392$
or, $\Rightarrow V a r (X) = 0.840$

Suggest Corrections

Similar questions

x

\begin{matrix} X & 0 & 1 & 2 & 3 & 4 P (X) & 0.1 & 0.25 & 0.3 & 0.2 & 0.15 \end{matrix}

X

X

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

X

P (X = x) = 0.1, 0.1, 0.1, 0.3, 0.4

(X = x) = 4, 3, 2, 1, 0

X

x

X = x_{i} : - 1, 0, + 1

p (X = x_{i}) : 0.4, 0.2, 0.4

X

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

k

Join BYJU'S Learning Program

$X = x$	$- 1.5$	$- 0.5$	$0.5$	$1.5$	$2.5$
$P [X = X]$	$0.05$	$0.2$	$0.15$	$0.25$	$0.35$