Mathematics · Limiting Distributions
Let {Xn : n ≥ 1} be a sequence of independent and identically distributed random variables, where X1 has an Exponential distribution with mean 1. Define Tn = max{X1, X2, ..., Xn} - ln n, n ≥ 1. Suppose Tn → Y in distribution as n → &infty;. Which of the following statements is true?
Verified Solution4 OptionsUpdated: October 2026👁️1 View
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- 1The derivative of the cumulative distribution function of Y at ln 3 is e-1/3.
- 2P(Y ≤ 0) = e-1.✓
- 3Median of Y = ln 2.
- 4Y has a Double Exponential distribution with location parameter ln(ln 2) and scale parameter 1.
Correct answer
P(Y ≤ 0) = e-1.
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