1Consider two random variables X1 and X2 with mean values mu

1.Consider two random variables X₁ and X₂ with mean values mu₁ = 10 and mu₂ = 2, respectively.

What is the numerical value of E(2X₁ - 3X₂)?

26

20

14

8

5

3.33

2.Consider two independent random variables X₁ and X₂ with standard deviation values sigma₁ = 6 and sigma₂ = 4, respectively.

What is the numerical value of V(2X₁ - 3X₂)?

0

2

10

20

52

288

3.Let X₁, X₂,

Solution

1. E(2X₁ - 3X₂) = 2E(X₁) - 3E(X₂) = 2*10 - 3*2 = 14

2. V(2X₁-3X₂) = 4V(X₁) + 9V(X₂) = 4*6² + 9*4² = 288

3. E(Xbar) = mu = 75

4. SD(Xbar) = SD / root(n) = 16 / root(64) = 16/8 = 2

5. All are true

E(Xbar) = mu

V(Xbar) = sigma^2 / n

E(T) = n(mu)

V(T) = n(sigma^2)

6. Var(Xbar) = Var(X)/n = (1/12)*1/100 = 1/1200

7. Expected value of Phat = 0.5