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2. Let X be a discrete random variable with pmf f(x) = log₁0 (²+¹), x = 1,2, ...,9. (This distribution, known as the Benford distribution, has been shown to accurately model the probabilities of the leading significant digit in numbers occurring in many datasets.) a) Verify that f(x) satisfies the conditions of a pmf. b) Find the cdf of X.

2. Let X be a discrete random variable with pmf f(x) = log₁0 (²+¹), x = 1,2, ...,9. (This distribution, known as the Benford distribution, has been shown to accurately model the probabilities of the leading significant digit in numbers occurring in many datasets.) a) Verify that f(x) satisfies the conditions of a pmf. b) Find the cdf of X.

Algebra & Trigonometry with Analytic Geometry
Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter10: Sequences, Series, And Probability
Section10.8: Probability
Problem 19E
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x = 1,2,...,9. (This 2. Let X be a discrete random variable with pmf f(x) = log₁0 distribution, known as the Benford distribution, has been shown to accurately model the probabilities of the leading significant digit in numbers occurring in many datasets.) a) Verify that f(x) satisfies the conditions of a pmf. b) Find the cdf of X.
Transcribed Image Text:x = 1,2,...,9. (This 2. Let X be a discrete random variable with pmf f(x) = log₁0 distribution, known as the Benford distribution, has been shown to accurately model the probabilities of the leading significant digit in numbers occurring in many datasets.) a) Verify that f(x) satisfies the conditions of a pmf. b) Find the cdf of X.
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