You visited us 1 times! Enjoying our articles? Unlock Full Access!

Probability Distribution

A random vari...

Question

A random variable $X$ has the following probability distribution:
$X$ $0$ $1$ $2$ $3$ $4$
$P (X)$ $0.1$ $k$ $2 k$ $2 k$ $k$
Determine:
(i) $k$
(ii) $P (X \geq 2)$ .

Open in App

Solution

(i) Since $\sum P (x) = 1$
$\Rightarrow 0.1 + k + 2 k + 2 k + k = 1$
or $6 k = 1 - 0.1$
$k = \frac{0.9}{6} \Rightarrow k = 0.15$
(ii) $P (x \geq 2) = P (x = 2) + P (x = 3) + P (x = 4)$
$= 2 k + 2 k + k$
$= 5 k = 5 (0.15)$
$P (x \geq 2) = 0.75$ .

Suggest Corrections

Similar questions

X

10 k

$X$	$- 2$	$- 1$	$0$	$1$	$2$	$3$
$P (X)$	$0.1$	$k$	$0.2$	$2 k$	$0.3$	$k$

X

$X$	$0$	$1$	$2$	$3$	$4$	$5$	$6$	$7$
$P (X)$	$0$	$k$	$2 k$	$2 k$	$3 k$	$k^{2}$	$2 k^{2}$	$7 k^{2} + k$

k

P (X < 3)

P (X > 6)

P (0 < X < 3)

X

$X = x$	$- 2$	$- 1$	$0$	$1$	$2$	$3$
$P (x)$	$\frac{1}{10}$	$K$	$\frac{1}{5}$	$2 K$	$\frac{3}{10}$	$K$

X

$X = x$	$0$	$1$	$2$	$3$	$4$	$5$	$6$	$7$
$P (X = x)$	$0$	$k$	$2 k$	$2 k$	$3 k$	$k^{2}$	$2 k^{2}$	$7 k^{2} + k$

k

P (0 < X < 5)

A random variable X has the following probability distribution.

$\begin{matrix} X & 0 & 1 & 2 & 3 & 4 & 5 & 6 & 7 P (X) & 0 & k & 2 k & 2 k & 3 k & k^{2} & 2 k^{2} & 7 k^{2} + k \end{matrix}$

P(X > 6)

Join BYJU'S Learning Program