Examine impact of using a truncated exponential distribution

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Reference no: EM131355475

1. In the exercise above, examine the impact of using a truncated exponential distribution Exp(λ) on the variance of the approximation of the tail probability.

2. Given an importance sample (X_i, f(X_i)/g(X_i)), show that if ω_i has a Poisson distribution ω_i ∼ P(f(X_i)/g(X_i)), the estimator

1/n Σⁿ_i=1 w_ih(x_i)

is unbiased. Deduce that the sample derived by this sampling mechanism is marginally distributed from f.

Reference no: EM131355475

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