Probability Distribution for Discrete Random Variables Solved Example #6

Looking for One-One Online Statistics coaching? Schedule a free discussion call with us. Mail: [email protected] Whatsapp: +91-9560560080 (Hourly Rates Starting $40 per hour) Our Online Coaching Page: https://www.eduspred.com/pages/help-microeconomics-econometrics-statistics-tutor Some of the Statistics courses we have helped students with: BEE2006: Statistics and Econometrics (University of Exeter) PSYC40122, PSYC49122: Advanced Experimentation and Statistics 1 (Nottingham Trent University) MT2504: Combinatorics and Probability (St. Andrews) ECON103: Quantitative Methods for Economics (Lancaster University) MT2508: Statistical Inference (St. Andrews) 153400121: Quantitative Methods for Economists (SOAS, University of London) EC3301: Statistics and Econometrics (University of St.Andrews) UN 1201: Statistics and Probability (Columbia University) Introduction to Statistics: Queenmary University These questions are taken from the book 'Probability and Statistics for Engineering and the Sciences' by Jay L. Devore (8th Edition) Complete set of Practice Questions for Discrete Random Variables: https://www.eduspred.com/courses/discrete-random-variables-probability-distributions-questions?coupon=yt10 Question 1: Suppose that you read through this year’s issues of the New York Times and record each number that appears in a news article— the income of a CEO, the number of cases of wine produced by a winery, the total charitable contribution of a politician during the previous tax year, the age of a celebrity, and so on. Now focus on the leading digit of each number, which could be 1, 2, . . . , 8, or 9. Your first thought might be that the leading digit X of a randomly selected number would be equally likely to be one of the nine possibilities (a discrete uniform distribution). However, much empirical evidence as well as some theoretical arguments suggest an alternative probability distribution called Benford’s law: p(x) = P 1st digit is x = log10 x + 1/x , x = 1,2,…..,9 a) Without computing individual probabilities from this formula, show that it specifies a legitimate pmf. b) Now compute the individual probabilities and compare to the corresponding discrete uniform distribution. c) Obtain the cdf of X. d) Using the cdf, what is the probability that the leading digit is at most 3? At least 5? 0:00 Introduction to Chapter 3- Probability Distribution for Discrete Random Variables 0:15 Introduction to Question 1 1:10 Part (a) 4:55 Part (b) 8:05 Part (c) 10:13 Part (d) Click here to view the entire playlist : https://www.youtube.com/playlist?list=PLyqDMruigg0LfOJxwXXldotlXrxSZot8K Website : http://www.eduspred.com/ SUBSCRIBE at: https://www.youtube.com/channel/UCyBh3AjZct_2JriA--Eamug?sub_confirmation=1 Facebook : https://www.facebook.com/Eduspread-Now-Eduspredcom-1972581306301312/ #discreterandomvariables #statistics #probabilitydistribution