Question

The probability distribution of a random variable X is given below:

X	0	1	2	3
P(X)	k	`"k"/2`	`"k"/4`	`"k"/8`

Determine the value of k.

Answer 1

We know that P(0) + P(1) + P(2) + P(3) = 1

⇒ `"k" + "k"/2 + "k"/4 + "k"/8` = 1

⇒ `(8"k" + 4"k" + 2"k" + "k")/8` = 1

⇒ 15k = 8

∴ k = `8/15`