3. Let Xi ∼ Poi(1), i = 1, . . . , n, be n = 20 independent Poisson r.v’s.Hint: you may use E(Y ) = λ and Var(Y ) = λ, for a Poisson r.v. Y ∼ Poi(λ).3a. Use the Markov inequality to obtain a bound on Pr (Ln Xi > 30) (±0.05 is okay).3b. Use the CLT to approximate the same probability (±0.01 is okay) 3. Let X;Poi(1), i = 1, ..., n, be n = 20 independent Poisson r.v's.Hint: you may use E(Y)= \ and Var(Y) = \, for a Poisson r.v. Y ~ Poi(A).3a. Use the Markov inequality to obtain a bound on Pr (- X; > 30) (±0.05 is okay).Pr (E1 X; > 30) <i=13b. Use the CLT to approximate the same probability (+0.01 is okay)Pr (E1 X; > 30) =i=1

Markov Inequality: If X is a nonnegative random variable and a > 0, then the probability that X…

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Let Xi ∼ Poi(1), i = 1, . . . , n, be n = 20 independent Poisson r.v’s.

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Question

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3. Let Xi ∼ Poi(1), i = 1, . . . , n, be n = 20 independent Poisson r.v’s.
Hint: you may use E(Y ) = λ and Var(Y ) = λ, for a Poisson r.v. Y ∼ Poi(λ).

3a. Use the Markov inequality to obtain a bound on Pr (Ln Xi > 30) (±0.05 is okay).

3b. Use the CLT to approximate the same probability (±0.01 is okay)

3. Let X;
Poi(1), i = 1, ..., n, be n = 20 independent Poisson r.v's.
Hint: you may use E(Y)= \ and Var(Y) = \, for a Poisson r.v. Y ~ Poi(A).
3a. Use the Markov inequality to obtain a bound on Pr (- X; > 30) (±0.05 is okay).
Pr (E1 X; > 30) <
i=1
3b. Use the CLT to approximate the same probability (+0.01 is okay)
Pr (E1 X; > 30) =
i=1

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