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A random variable $x$ has the following probability distribution:
$X = x$ 0 1 2 3 4 5 6 7 8
$P (X = x)$ $a$ $3 a$ $5 a$ $7 a$ $9 a$ $11 a$ $13 a$ $15 a$ $17 a$
Statement I : The value of $' a'$ is $\frac{1}{81}$
Statement II : Mean of random variable $X$ is 6

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Statement I and statement II both are true

Statement I is true and Statement II is false

Statement I is false and Statement II is true

Statement I and statement II both are false

answer is A.

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Detailed Solution

$Σ P (X = x_{i}) = 1 \Rightarrow 81 a = 1 \Rightarrow a = \frac{1}{81}$

Mean $= μ = Σ x_{i} P (X = x_{i}) = 5.48$

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