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

E(2X₁ - 3X₂) = 2E(x1) -3E(x2) =

14

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V(2X₁ - 3X₂) = 2²(6²)+3²(4²) =

144+144= 288

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E(Xbar) = 75

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standard deviation of Xbar = 16/8 =2

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These three are true

E(Xbar) = mu

V(Xbar) = sigma^2 / n

E(T) = n(mu)

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6) 10,000/12 is answer

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7) expected value (mean) of Phat = 50