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

Question

A random variable X has the following probability distribution:

Values of X:	-2	-1	0	1	2	3
P(X)	0.1	k	0.2	2k	0.3	k

Find the value of k.

✓

Answer

Here,

Values of X:	-2	-1	0	1	2	3
P(X)	0.1	k	0.2	2k	0.3	k

We know that,
P(-2) + P(-1) + P(0) + P(1) + P(2) + P(3) = 1
⇒ 0.1 + k + 0.2 + 2k + 0.3 + k = 1
⇒ 4k + 0.6 = 1
⇒ 4k = 1 - 0.6
⇒ 4k = 0.4
$\Rightarrow\text{k}=\frac{0.4}{4}$
$\Rightarrow\text{k}=\frac{1}{10}$
$\Rightarrow\text{k}=0.1$

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