Question

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

X = k	0	1	2	3	4
P(X = k)	0.1	0.4	0.3	0.2	0

The variance of X is ______

Options

• 1.6

• 0.24

• 0.84

• 0.75

Answer 1

0.84

Explanation:

E(X) = `sumx_i . P(x_i)`

= 0(0.1) + 1(0.4) + 2(0.3) + 3(0.2) + 4(0)

= 0 + 0.4 + 0.6 + 0.6 + 0

= 1.6

Variance = E (X²) - [E(X)]²

= 0²(0.1) + 1²(0.4) + 2²(0.3) + 3²(0.2) + 4²(0) - 1.6²

= 0 + 0.4 + 1.2 + 1.8 - 2.56

= 0.84