b) (i) The probability distribution of the number of customers visiting a specialty store each hour, N, is as follows: n Pr ( N = n ) 5 0.1785 6 k 7 0.3105 8 0.1115 9 0.015 Find the value of k which makes this a valid distribution. (ii) In a certain mechanical component, the time to failure T (in hours) is distributed with the probability density function f(t) = 2.5 t^−3.5 for t ≥ 1. Calculate the mean E(T) of this variable. (iii) In the case of part (ii), E(T^2 ) = 5. Calculate Var(T) of the variable T based on this information

b) (i) The probability distribution of the number of customers visiting a specialty store each hour, N, is as follows: n Pr ( N = n ) 5 0.1785 6 k 7 0.3105 8 0.1115 9 0.015 Find the value of k which makes this a valid distribution. (ii) In a certain mechanical component, the time to failure T (in hours) is distributed with the probability density function f(t) = 2.5 t^−3.5 for t ≥ 1. Calculate the mean E(T) of this variable. (iii) In the case of part (ii), E(T^2 ) = 5. Calculate Var(T) of the variable T based on this information

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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