Question

A random variable x has the following probability distribution :

x	0	1	2	3	4	5	6
P( X = x)	k	3k	5k	7k	9k	11k	13k

Find k.

Answer 1

∵ `sum_(l = 0)^6` P(X) = 1
∴ P(0) + P(1) + P(2) + P(3) + P(4) + P(5) + P(6) = 1

∴ k + 3k + 5k + 7k + 9k + 11k + 13k = 1

∴ 49k = 1

∴ k = `1/49`