MATH264: Practical Questions Week 9 (Thursday)
3. The random variables X1, X2, . . . are independent and identically distributed with the Probability
Mass Function Pr(X = −1) = Pr(X = 3) = 0.5.
(a) Calculate µ = E(X) and σ2 = V ar(X).
(b) For the case n = 200 use the Central Limit Theorem to approximate the probability Pr{ln(X¯) >
0}, where
X¯ = (1/200)
200∑
i=1
Xi
is the sample mean and ln denotes the natural logarithm (i.e., logarithm with base e).
(c) Find the minimum n for which
Pr
{ n∑
i=1
Xi > 190
}
> 0.99.
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