Question

A random variable x has to following probability distribution.

X	0	1	2	3	4	5	6	7
P(x)	0	k	2k	2k	3k	k2	2k2	7k2 + k

Determine

Options

• `3/10`

• `17/100`

• `2/10`

• `1/10`

Answer 1

`1/10`

Explanation:

Sum of probabilities = 1

i.e., 0 + k + 2k + 2k + 3k + k² + 2k² + 7k² + k = 1

or 10k² + 9k = 1 or 10k² + 9k – 1 = 0

(k + 1) (10k – 1) = 0

∴ k = – 1 or k = `1/10`

∴ k ≠ – 1 

∴ k = `1/10`