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Probability Distribution

A random vari...

Question

A random variable $X$ has the following probability distribution. Find the value of $10 k$ .
$X$ $- 2$ $- 1$ $0$ $1$ $2$ $3$
$P (X)$ $0.1$ $k$ $0.2$ $2 k$ $0.3$ $k$

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Solution

The correct option is A 1
As we know that $\sum P (X) = 1$
$⟹ 0.1 + k + 0.2 + 2 k + 0.3 + k = 1 ⟹ k = 0.1 ⟹ 10 k = 1$

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X

$X$	$0$	$1$	$2$	$3$	$4$
$P (X)$	$0.1$	$k$	$2 k$	$2 k$	$k$

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P (X \geq 2)

$X = x$	$- 2$	$- 1$	$0$	$1$	$2$	$3$
$P (X = x)$	$0.1$	$K$	$0.2$	$2 K$	$0.3$	$K$

X

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

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

E (x) =

X

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

k

X

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