If a random variable X has the following probability distribution: X : 0 1 2 3 4 5 6 7 8 P (X) : a 3a 5a 7a 9a 11a 13a 15a 17a then the value of a is

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$\frac{1}{81}$ We know that the sum of probabilities in a probability distribution is always 1. $\therefore$ P (X = 0) + 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 a + 3a + 5a + 7a + 9a + 11a + 13a + 15a + 17a = 1 \Rightarrow 81a = 1 \Rightarrow a = $\frac{1}{81}$

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