Question

Consider the sample space S = -3, -1.5, 0, 1.5, 3 with probability values P(-3) = 0.1 , P(-1.5) = 0.2 , P(0) = γ , P(1.5) = 0.1 . Calculate γ and then find E(S) .

a) γ = 0.1, quad E(S) = -0.6

b) γ = 0.4, quad E(S) = 0

c) γ = 0.2, quad E(S) = 0

d) γ = 0.1, quad E(S) = 0.6

Answer 1

To find the value of γ (gamma), we need to use the fact that the probabilities in the sample space S must sum to 1. We can write the equation: 0.1 + 0.2 + γ + 0.1 = 1. Solving for γ, we get γ = 0.6. To find the expected value (E) of S, we need to multiply each value in the sample space by its respective probability and sum the results. E(S) = (-3)(0.1) + (-1.5)(0.2) + (0)(0.6) + (1.5)(0.1) + (3)(0) = -0.6.

Step-by-step explanation:

To find the value of γ (gamma), we need to use the fact that the probabilities in the sample space S must sum to 1. We know that P(-3) = 0.1, P(-1.5) = 0.2, P(0) = γ, and P(1.5) = 0.1. So, we can write the equation: 0.1 + 0.2 + γ + 0.1 = 1. Solving for γ, we get γ = 0.6.

Next, to find the expected value (E) of S, we need to multiply each value in the sample space by its respective probability and sum the results.

E(S) = (-3)(0.1) + (-1.5)(0.2) + (0)(0.6) + (1.5)(0.1) + (3)(0) = -0.6.