Question

A random variable X has the following probability distribution : 

X = x	-2	-1	0	1	2	3
P(x)	0.1	k	0.2	2k	0.3	k

Find the value of k and calculate mean. 

Answer 1

As the given table is probability distribution table : 

∑p_i = 1

∴ 0.1 + k + 0.2 + 2k + 0.3 + k = 1

∴ 0.6 + 4k = 1

∴ 4k = 1 - 0.6

∴ 4k = 0.4

∴ k = 0.1 

k = 0.1

X = x	-2	-1	0	1	2	3
P(x)	0.1	0.1	0.2	0.2	0.3	0.1

E (X) (mean) = ∑p_i x_i 

= - 0.2 - 0.1 + 0 + 0.2 + 0.6 + 0.3

= 0.8

∴ k = 0.1 and E(X) = 0.8