Question

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

(a) $\frac{7}{81}$

(b) $\frac{5}{81}$

(c) $\frac{2}{81}$

(d) $\frac{1}{81}$

Answer 1

(d) $\frac{1}{81}$


We know that the sum of probabilities in a probability distribution is always 1.

∴ 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

$$\begin{gathered} \Rightarrow a+3a+5a+7a+9a+11a+13a+15a+17a=1 \\ \Rightarrow 81a=1 \\ \Rightarrow a=\frac{1}{81} \end{gathered}$$