The discrete random variable Z has the following discrete random variable distribution. What is E([Z-2]^2)?

Question

Answer 1

The probabilities won't change, just the values.

[1-2]^2 = 1

[2-2]^2 = 0

[3-2]^2 = 1

[4-2]^2 = 4

The expected value is the sum of the products of values and probabilities.

E([Z-2]^2) = (1)(0.2) + (0)(0.4) + (1)(0.3) + (4)(0.1)

E([Z-2]^2) = 0.2+0+0.3+0.4 = 0.9