Just to give you a break from all the integrals, here is a mixture distribution problem abouttwo discrete random variables.Suppose I have three dice in my pocket: two fair dice that land on 6 with probability 16, and a loaded die that lands on 6 with probability 1/2. I take a random die out of my pocket, rollit 10 times, and count the number of sixes rolled. Let N be the result I get.(a) Describe the distribution of N as a mixture of two distributions we know, and give theweights used in the mixture.(b) What is E[N]?(c) What is Pr[N = 0]?
Just to give you a break from all the integrals, here is a mixture distribution problem abouttwo discrete random variables.Suppose I have three dice in my pocket: two fair dice that land on 6 with probability 16, and a loaded die that lands on 6 with probability 1/2. I take a random die out of my pocket, rollit 10 times, and count the number of sixes rolled. Let N be the result I get.(a) Describe the distribution of N as a mixture of two distributions we know, and give theweights used in the mixture.(b) What is E[N]?(c) What is Pr[N = 0]?
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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Just to give you a break from all the integrals, here is a mixture distribution problem about
two discrete random variables.
Suppose I have three dice in my pocket: two fair dice that land on 6 with
6, and a loaded die that lands on 6 with probability 1/2. I take a random die out of my pocket, roll
it 10 times, and count the number of sixes rolled. Let N be the result I get.
(a) Describe the distribution of N as a mixture of two distributions we know, and give the
weights used in the mixture.
(b) What is E[N]?
(c) What is Pr[N = 0]?
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