Question

Find the expected value of a random variable which has the following probability distribution?

X:	2	4	6	8	10
P:	0.1	0.3	0.4	0.1	0.1

1. 5.2
2. 5.4
3. 5.6
4. 5.8

Answer 1

Correct Answer - Option 3 : 5.6

Calculation

We know expected value of random variable

f(x) = ∑x_ip_i

where I = 1, 2, 3,-----n

f(x) = P₁x₁ + P₂x₂ + P₃x₃ + P₄x₄ + P₅x₅

⇒ f(x) = 0.1 × 2 + 0.3 × 4 + 0.4 × 6 + 0.1 × 8 + 0.1 × 10

⇒ 0.2 + 1.2 + 2.4 + 0.8 + 1

∴ f(x) = 5.6