3. A coin is tossed repeatedly, with heads turning up with probability p on each toss. Let N be the minimum number of tosses required to obtain k heads. Show that, as p↓ 0, the distribution function of 2Np converges to that of a gamma distribution.

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.
Chapter13: Probability And Calculus
Section13.3: Special Probability Density Functions
Problem 36E
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3. A coin is tossed repeatedly, with heads turning up with probability p on each toss. Let N be the
minimum number of tosses required to obtain k heads. Show that, as p↓ 0, the distribution function
of 2Np converges to that of a gamma distribution.
Transcribed Image Text:3. A coin is tossed repeatedly, with heads turning up with probability p on each toss. Let N be the minimum number of tosses required to obtain k heads. Show that, as p↓ 0, the distribution function of 2Np converges to that of a gamma distribution.
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