a) On the throw of a fair die, the expected value of the number showing is...

a) On the throw of a fair die, the expected value of the number showing is 3.5 and the standard deviation is 1.71. What is the expected value and standard deviation of the sum of the values from the throw of a pair of dice

b) Suppose Y₁ and Y₂ are independent, Var(Y₁) = Var(Y₂) = σ_y² and Z₁ = Y₁+Y₂ .What is Var(Z₁)? How does this compare to the result found in part a)?

c) Generalize the previous results. Suppose Y₁, Y₂, · · · , Y_n are independent, Var(Y₁) = Var(Y₂) = · · · = Var(Y_n) = σ²_y and Z₂ = Y₁ + Y₂ + · · · + Y_n. What is Var(Z₂)?

d) Again, let’s keep generalizing these results. Suppose Y₁, Y₂, · · · , Y_n are independent, Var(Y₁) = Var(Y₂) = · · · = Var(Y_n) = σ²_y and Z₃ = 1/n (Y₁ + Y₂ + · · · + Y_n). What is Var(Z₃)?

Expert Solution

orchestra answered 1 year ago

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