Independent trials that result in a success with probability p are successively performed until a total of r successes is obtained.Let X= # of trials that are needed (total number, including the r successes).In the following questions please mark the correct answer. Use q=1-p.Find E(X).Hint:You might find it useful to use a geometric series with 0 <*< 1,s =E" = (1– m) ',and the order k derivativeCn (n – 1).. (n – k + 1) ="-* = k!/(1 – #)**.1/pnpnpr/pO (n – 1)pnone of these

Given information: Given that the independent trials results in a success with probability p are…

Independent trials that result in a success with probability p are successively performed until a total of r successes is obtained. Let X= # of trials that are needed (total number, including the r successes).

Independent trials that result in a success with probability p are successively performed until a total of r successes is obtained. Let X= # of trials that are needed (total number, including the r successes).

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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Question

Independent trials that result in a success with probability p are successively performed until a total of r successes is obtained.
Let X= # of trials that are needed (total number, including the r successes).
In the following questions please mark the correct answer. Use q=1-p.
Find E(X).
Hint:
You might find it useful to use a geometric series with 0 <*< 1,
s =E" = (1– m) ',
and the order k derivative
Cn (n – 1).. (n – k + 1) ="-* = k!/(1 – #)**.
1/p
np
np
r/p
O (n – 1)p
none of these

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