A random variable has the following probability distribution: X = x_i 0 1 2 3 4 5 6 7 P(X = X_i) 0 2p 2p 3p p^2 2p^2 7p^2 7p^2 2p

A random variable has the following probability distribution: X =…

MCQ

A random variable has the following probability distribution:

$X = x_i$	$0$	$1$	$2$	$3$	$4$	$5$	$6$	$7$
$P(X = X_i)$	$0$	$2p$	$2p$	$3p$	$p^2$	$2p^2$	$7p^2$	$7p^2$	$2p$

✓
$\frac{1}{10}$
B
$-1$
C
$-\frac{1}{10}$
D
$\frac{1}{5}$

✓

Answer

Correct option: A.

$\frac{1}{10}$

We know that the sum of probabilities in a probability distribution is always $1$.
$\therefore P(X = 1) + P(X = 2) + P(X = 3) + P(X = 4) + P(X = 5) +P(X = 6) + P(X = 7) +P(X = 8) = 1$
$\Rightarrow 0 + 2p + 2p + 3p + p^2 + 2p^2 + 7p^2 + 2p = 1$
$\Rightarrow 10p^2+ 9p - 1 = 0$
$\Rightarrow (10p - 1)(p + 1) = 0$
$\Rightarrow\text{p}=\frac{1}{10}\text{ or }-1 \ ($Negleting $-1$ as the value of the probability cannot be negative$)$

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