A random variable $X$ has the following probability distribution
$X = x : 1234$
$p (X = x) : 0.4 0.3 0.2 0.1$ , then its mean is

4

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3

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2

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1

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Solution

The correct option is A $2$
Here, $n = 4$ , $P (X = 1) = 0.4, P (X = 2) = 0.3, P (X = 3) = 0.2, P (X = 4) = 0 .1$

We know, $P (X = r) =^{n} C_{r} p^{r} q^{n - r}$

$\Rightarrow P (X = 1) =^{4} C_{1} p q^{3} = .4 \Rightarrow p q^{3} = 0 .1$ ..(i)

$\Rightarrow P (X = 4) =^{4} C_{4} p q^{3} = .1 \Rightarrow p^{3} q = 0.1$ ..(ii)

Divide (i) and (ii)

$\frac{p^{3} q}{p q^{3}} = 1 \Rightarrow p^{2} = q^{2} \Rightarrow p = q$

$p = q = \frac{1}{2}$ , since $p + q = 1$

Hence mean $= n p = 4 \cdot \frac{1}{2} = 2$

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