7. A spinner from a board game randomly indicates a real number between 0 and 10. The spinner is fair in the sense that it indi- cates a number in a given interval with the same probability as it indicates a number in any other interval of the same length. (a) Explain why the function (0.1 if 0 < x< 10 f(x) if x <0 or x> 10 is a probability density function for the spinner's values. (b) What does your intuition tell you about the value of the mean? Check your guess by evaluating an integral.
7. A spinner from a board game randomly indicates a real number between 0 and 10. The spinner is fair in the sense that it indi- cates a number in a given interval with the same probability as it indicates a number in any other interval of the same length. (a) Explain why the function (0.1 if 0 < x< 10 f(x) if x <0 or x> 10 is a probability density function for the spinner's values. (b) What does your intuition tell you about the value of the mean? Check your guess by evaluating an integral.
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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
Transcribed Image Text:7. A spinner from a board game randomly indicates a real number
between 0 and 10. The spinner is fair in the sense that it indi-
cates a number in a given interval with the same probability as
it indicates a number in any other interval of the same length.
(a) Explain why the function
[0.1 if 0<x < 10
f(x) :
if x <0 or x> 10
is a probability density function for the spinner's values.
(b) What does your intuition tell you about the value of the
mean? Check your guess by evaluating an integral.
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