Question

Given the following probability distribution, what is the expected value of the random variable X? X P(X) 100 .10 150 .20 200 .30 250 .30 300 .10 Sum1.00 Multiple Choice 175 150 200 205

Answer 1

d) 205

Explanation:

Step(i):-

x : 100 150 200 250 300

p(X=x) : 0.10 0.20 0.30 0.30 0.10

Step(ii):-

Let 'X' be the discrete random variable

Expected value of the random variable

E(X) = ∑ x P(X=x)

= 100 X 0.10 + 150 X 0.20 + 200 X 0.30 +250 X 0.30 + 300 X 0.10

= 205

Final answer:-

The expected value E(X) = 205