1)What is the following probabilities for a series of coin tosses:• A. 20 flips, 4 heads• B. 50 flips,10 heads• C. 50 flips,20 headsD. Plot the expected number of heads as a function of the number of the numberOf heads for a set of 100 coin flips.e)Show a proof by induction for the equation, the factorial integral.x"e- dx.f) Calculate (via numerical integration or other method) thevalue of the gamma function for n=10.5 & n=11.5. ThenCompare the values to the factorial integral valuesfor n=10,11 & 12.

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A First Course in Probability (10th Edition)

10th Edition

ISBN:9780134753119

Author:Sheldon Ross

Publisher:Sheldon Ross

Chapter1: Combinatorial Analysis

Section: Chapter Questions

Problem 1.1P: a. How many different 7-place license plates are possible if the first 2 places are for letters and...

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1)What is the following probabilities for a series of coin tosses: • A. 20 flips, 4 heads • B. 50 flips, 10 heads • C. 50 flips,20 heads