Homework Help is Here – Start Your Trial Now!
Math
Probability
(c) What are the parameters a and 3 of the beta dis- tribution illustrated here? (d) The mean of the beta distribution is . What is the mean proportion of impurities in the batch? a+B (e) The variance of a beta distributed random variable is αβ = (a + 3)²(a+3+1)* What is the variance of Y in this problem?

(c) What are the parameters a and 3 of the beta dis- tribution illustrated here? (d) The mean of the beta distribution is . What is the mean proportion of impurities in the batch? a+B (e) The variance of a beta distributed random variable is αβ = (a + 3)²(a+3+1)* What is the variance of Y in this problem?

A First Course in Probability (10th Edition)
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...
See similar textbooks
icon
Related questions
Question
100%

I need help with parts c to e please

Impurities in batches of product of a chemical process reflect a serious problem. It is known that the proportion of impurities Y in a batch has the following density function. Complete parts (a) through (e) below. f(y)= [9(1-y)³, 0≤y≤1, = 1911-1 elsewhere O A. The given function is a valid density function because 9(1 - y) dy = | 0 B. The given function is a valid density function because it is at least 0 everywhere. The given function is a valid density function because it is at least 0 everywhere and because √(1-y)² 0 9(1 - y) dy = 1. (b) A batch is considered not sellable and then not acceptable if the percentage of impurities exceeds 60%. What is the probability that a batch is considered not acceptable (i.e., Y> 0.6)? The probability is 0.0003. (Round to four decimal places as needed.) (c) What are the parameters & and ß of the beta distribution illustrated here? α= (Type an integer or a decimal. Do not round.)
Transcribed Image Text:Impurities in batches of product of a chemical process reflect a serious problem. It is known that the proportion of impurities Y in a batch has the following density function. Complete parts (a) through (e) below. f(y)= [9(1-y)³, 0≤y≤1, = 1911-1 elsewhere O A. The given function is a valid density function because 9(1 - y) dy = | 0 B. The given function is a valid density function because it is at least 0 everywhere. The given function is a valid density function because it is at least 0 everywhere and because √(1-y)² 0 9(1 - y) dy = 1. (b) A batch is considered not sellable and then not acceptable if the percentage of impurities exceeds 60%. What is the probability that a batch is considered not acceptable (i.e., Y> 0.6)? The probability is 0.0003. (Round to four decimal places as needed.) (c) What are the parameters & and ß of the beta distribution illustrated here? α= (Type an integer or a decimal. Do not round.)
(c) What are the parameters a and 3 of the beta dis- tribution illustrated here? (d) The mean of the beta distribution is . What is the mean proportion of impurities in the batch? a+B (e) The variance of a beta distributed random variable is αβ = (a +3)²(a+3+1)* What is the variance of Y in this problem?
Transcribed Image Text:(c) What are the parameters a and 3 of the beta dis- tribution illustrated here? (d) The mean of the beta distribution is . What is the mean proportion of impurities in the batch? a+B (e) The variance of a beta distributed random variable is αβ = (a +3)²(a+3+1)* What is the variance of Y in this problem?
Expert Solution
trending now

Trending now

This is a popular solution!

steps

Step by step

Solved in 5 steps

SEE SOLUTIONCheck out a sample Q&A here
Blurred answer