Let X1, X2, ... Xn be iid random variables with common pdf f(x) = { e^-(x-?) x > ? , -8 { 0 elsewhere This pdf is called the shifted exponential. Let Yn = min{ X1, X2, ......

Let X1, X2, ... Xn be iid random variables with common pdf

f(x) = { e^-(x-?) x > ? , -8

{ 0 elsewhere

This pdf is called the shifted exponential. Let Yn = min{ X1, X2, ......

Answered Same DayDec 23, 2021

Answer To: Let X1, X2, ... Xn be iid random variables with common pdf f(x) = { e^-(x-?) x > ? , -8 { 0...

David answered on Dec 23 2021

121 Votes

Let X1, X2, ... Xn be iid random variables with common pdf

f(x) = { e^-(x-θ) x > θ , -∞ < θ < ∞
{ 0 elsewhere
This pdf is called the shifted exponential. Let Yn = min{ X1, X2, .... Xn}.
Prove that Yn ---> θ in probability by obtaining the cdf and pdf of Yn.

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Let X1, X2, ... Xn be iid random variables with common pdf f(x) = { e^-(x-?) x > ? , -8 { 0 elsewhere This pdf is called the shifted exponential. Let Yn = min{ X1, X2, ......

Answer To: Let X1, X2, ... Xn be iid random variables with common pdf f(x) = { e^-(x-?) x > ? , -8 { 0...

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