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 ofimpurities Y in a batch has the following density function. Complete parts (a) through (e) below.f(y)= [9(1-y)³, 0≤y≤1,= 1911-1elsewhereO A. The given function is a valid density function because 9(1 - y) dy = |0B. 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)²09(1 - y) dy = 1.(b) A batch is considered not sellable and then not acceptable if the percentage of impurities exceeds 60%. Whatis 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 isthe mean proportion of impurities in the batch?a+B(e) The variance of a beta distributed random variableisαβ= (a +3)²(a+3+1)*What is the variance of Y in this problem?

Given that : Y: Impurities in batches of product of a chemical process reflect a serious…

(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)

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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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.)

(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?

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