Can you help please: Suppose that X ∼ Geom(p). In chapter 2, we computed the CDF of X as FX(x) = 1 − (1 − p) x , for x = 1, 2, · · · . If p = λ/n, show that Y = X/n converges to an exponential distribution with parameter λ as n → ∞.

Can you help please: Suppose that X ∼ Geom(p). In chapter 2, we computed the CDF of X as FX(x) = 1 − (1 − p) x , for x = 1, 2, · · · . If p = λ/n, show that Y = X/n converges to an exponential distribution with parameter λ as n → ∞.

Calculus For The Life Sciences

2nd Edition

ISBN:9780321964038

Author:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.

Publisher:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.

Chapter3: The Derivative

Section3.3: Rates Of Change

Problem 30E: If the instantaneous rate of change of f(x) with respect to x is positive when x=1, is f increasing...

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Question

Can you help please:

Suppose that X ∼ Geom(p). In chapter 2, we computed the CDF of X as FX(x) = 1 − (1 − p)
x
,
for x = 1, 2, · · · . If p = λ/n, show that Y = X/n converges to an exponential distribution with
parameter λ as n → ∞.

Expert Solution