Answered: (1) What is the probability that…

(1) What is the probability that exactly 6 of the characters are digits? (2) What is the expected number of digits in a sequence? (3) What is the variance of the number of digits in a sequence?

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

The exam will consist of a 10-character sequence which students will have to write in stats class. They will have a machine select each character of the sequence independently and uniformly at random from {a, b, . . . , z}∪{A, B, . . . , Z}∪{0, 1, . . . , 9} right before the exam:

(1) What is the probability that exactly 6 of the characters are digits?

(2) What is the expected number of digits in a sequence?

(3) What is the variance of the number of digits in a sequence?

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