Explanation From the given information, Θ follows uniform distribution on the interval [ − π 2 , π 2 ] . The pdf of Θ is f ( Θ ) = 1 π 2 − ( − π 2 ) = 1 π 2 + π 2 = 1 π Let X = tan Θ The cdf of the tan Θ is given as follows: F ( x ) = P ( X ≤ x ) = P ( tan Θ ≤ x ) = P ( Θ ≤ tan − 1 x ) = ∫ − π 2 tan − 1 x f ( Θ ) d Θ = ∫ − π 2 tan − 1 x 1 π d Θ = 1 π ( Θ ) − π 2 tan<

Mathematical Statistics and Data Analysis

3rd Edition

ISBN: 9781111793715

Author: John A. Rice

Publisher: Cengage Learning

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Definition Definition Probability of occurrence of a continuous random variable within a specified range. When the value of a random variable, Y, is evaluated at a point Y=y, then the probability distribution function gives the probability that Y will take a value less than or equal to y. The probability distribution function formula for random Variable Y following the normal distribution is: F(y) = P (Y ≤ y) The value of probability distribution function for random variable lies between 0 and 1.

Chapter 2.5, Problem 63P

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Compute the cdf of tanΘ when Θ follows a uniform distribution on the interval [−π2,π2].

Compute the pdf of tanΘ when Θ follows a uniform distribution on the interval [−π2,π2].

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Mathematical Statistics and Data Analysis

Ch. 2.5 - Prob. 1P Ch. 2.5 - Prob. 2P Ch. 2.5 - Prob. 3P Ch. 2.5 - Prob. 4P Ch. 2.5 - Prob. 5P Ch. 2.5 - Prob. 6P Ch. 2.5 - Prob. 7P Ch. 2.5 - Prob. 8P Ch. 2.5 - Prob. 9P Ch. 2.5 - Prob. 10P

Ch. 2.5 - Prob. 11P Ch. 2.5 - Prob. 12P Ch. 2.5 - Prob. 13P Ch. 2.5 - Prob. 14P Ch. 2.5 - Prob. 15P Ch. 2.5 - Prob. 17P Ch. 2.5 - Prob. 18P Ch. 2.5 - Prob. 19P Ch. 2.5 - Prob. 20P Ch. 2.5 - Prob. 21P Ch. 2.5 - Prob. 22P Ch. 2.5 - Prob. 23P Ch. 2.5 - Prob. 24P Ch. 2.5 - Prob. 25P Ch. 2.5 - Prob. 26P Ch. 2.5 - Prob. 27P Ch. 2.5 - Prob. 28P Ch. 2.5 - Prob. 29P Ch. 2.5 - Prob. 30P Ch. 2.5 - Prob. 31P Ch. 2.5 - Prob. 32P Ch. 2.5 - Prob. 33P Ch. 2.5 - Prob. 34P Ch. 2.5 - Prob. 35P Ch. 2.5 - Prob. 36P Ch. 2.5 - Prob. 37P Ch. 2.5 - Prob. 38P Ch. 2.5 - Prob. 39P Ch. 2.5 - Prob. 40P Ch. 2.5 - Prob. 41P Ch. 2.5 - Prob. 42P Ch. 2.5 - Prob. 43P Ch. 2.5 - Prob. 44P Ch. 2.5 - Prob. 45P Ch. 2.5 - Prob. 46P Ch. 2.5 - Prob. 47P Ch. 2.5 - Prob. 48P Ch. 2.5 - Prob. 49P Ch. 2.5 - Prob. 50P Ch. 2.5 - Prob. 51P Ch. 2.5 - Prob. 52P Ch. 2.5 - Prob. 53P Ch. 2.5 - Prob. 54P Ch. 2.5 - Prob. 55P Ch. 2.5 - Prob. 56P Ch. 2.5 - Prob. 57P Ch. 2.5 - Prob. 58P Ch. 2.5 - Prob. 59P Ch. 2.5 - Prob. 60P Ch. 2.5 - Prob. 61P Ch. 2.5 - Prob. 62P Ch. 2.5 - Prob. 63P Ch. 2.5 - Prob. 64P Ch. 2.5 - Prob. 65P Ch. 2.5 - Prob. 66P Ch. 2.5 - Prob. 67P Ch. 2.5 - Prob. 68P Ch. 2.5 - Prob. 69P Ch. 2.5 - Prob. 70P

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Compute the cdf of tan Θ when Θ follows a uniform distribution on the interval [ − π 2 , π 2 ] . Compute the pdf of tan Θ when Θ follows a uniform distribution on the interval [ − π 2 , π 2 ] .

Solution Summary: The author calculates the cdf of mathrmtanTheta when it follows a uniform distribution on the interval

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Compute the cdf of tanΘ when Θ follows a uniform distribution on the interval [−π2,π2].

Compute the pdf of tanΘ when Θ follows a uniform distribution on the interval [−π2,π2].

Chapter 2 Solutions

Compute the cdf of tan Θ when Θ follows a uniform distribution on the interval [ − π 2 , π 2 ] . Compute the pdf of tan Θ when Θ follows a uniform distribution on the interval [ − π 2 , π 2 ] .

Solution Summary: The author calculates the cdf of mathrmtanTheta when it follows a uniform distribution on the interval

Concept explainers

Videos

Compute the cdf of tanΘ when Θ follows a uniform distribution on the interval [−π2,π2]. Compute the pdf of tanΘ when Θ follows a uniform distribution on the interval [−π2,π2].

Chapter 2 Solutions

Compute the cdf of tanΘ when Θ follows a uniform distribution on the interval [−π2,π2].

Compute the pdf of tanΘ when Θ follows a uniform distribution on the interval [−π2,π2].