If a random variable has the probability distribution 0 1 2 3 4 5 6 7 0 then is equal to [2026]

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Solution

Q.
If a random variable $x$ has the probability distribution

$x$ 0 1 2 3 4 5 6 7

$P (x)$ 0 $2 k$ $k$ $3 k$ $2 k^{2}$ $2 k$ $k^{2} + k$ $7 k^{2}$

then $P (3 < x \leq 6)$ is equal to [2026]

1 0.64

2 0.34

3 0.33

4 0.22

Ans.
(3)

$\sum P (x_{i}) = 1$

$\Rightarrow 9 k + 10 k^{2} = 1$

$\Rightarrow 10 k^{2} + 9 k - 1 = 0 \Rightarrow k = \frac{1}{10}$

$P (3 < x \leq 6) = 3 k + 3 k^{2}$

$= \frac{3}{10} + \frac{3}{100} = 0.33$

$= 0.33$

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