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

Options

•  \[\frac{7}{81}\]

   

•  \[\frac{5}{81}\]

   

• \[\frac{2}{81}\] 

   

• \[\frac{1}{81}\]

   

Answer 1

\[\frac{1}{81}\]

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

\[\Rightarrow a + 3a + 5a + 7a + 9a + 11a + 13a + 15a + 17a = 1\]
\[ \Rightarrow 81a = 1\]
\[ \Rightarrow a = \frac{1}{81}\]