a. Flip a balanced coin 5000 times. Let X be the total number of heads. Compute P(2400 ≤ X ≤ 2600). b. Let X1,··,Xn be identically and independently observed with the common expected value µ = E(Xi) = 0.7 and the common variance σ2 = V(Xi) = 1.9. Compute P(0.69 ≤ X¯ ≤ 0.71) for n = 103, 104, and 105, respectively. c. Let X1,··,X1000 be identically and independently observed with the common PMF given by __________________________ x 1 2 3 4 -------------------------------------------- p(x) 0.25 0.15 0.2 0.4 __________________________ Compute P(2.70 ≤ X¯ ≤ 2.80).
[Hint: Use the Central Limit Theorem to compute the following probabilities].
a. Flip a balanced coin 5000 times. Let X be the total number of heads. Compute P(2400 ≤ X ≤ 2600).
b. Let X1,··,Xn be identically and independently observed with the common expected value µ = E(Xi) = 0.7 and the common variance σ2 = V(Xi) = 1.9. Compute P(0.69 ≤ X¯ ≤ 0.71) for n = 103, 104, and 105, respectively.
c. Let X1,··,X1000 be identically and independently observed with the common PMF given by
__________________________
x 1 2 3 4
--------------------------------------------
p(x) 0.25 0.15 0.2 0.4
__________________________
Compute P(2.70 ≤ X¯ ≤ 2.80).
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