Suppose a special type of small data processing firm is so specialized that some have difficulty making a profit in their first year of operation. The probability density function that characterizes the proportion Y that make a profit is given by ky² ( 1 – y)³ 0

Calculus For The Life Sciences
2nd Edition
ISBN:9780321964038
Author:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.
Publisher:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.
Chapter13: Probability And Calculus
Section13.CR: Chapter 13 Review
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Suppose a special type of small data processing firm is so specialized that some have difficulty making a profit in their first year of
operation. The probability density function that characterizes the proportion Y that make a profit is given by
ky² ( 1 - y)3
0<y<1
f(y)=
elsewhere
(a) What is the value of k that renders the above a valid density function?
(b) Find the probability that at least 75% of the firms make a profit in the first year.
(C) Find the expected proportion of profit and variance of X.
Transcribed Image Text:Suppose a special type of small data processing firm is so specialized that some have difficulty making a profit in their first year of operation. The probability density function that characterizes the proportion Y that make a profit is given by ky² ( 1 - y)3 0<y<1 f(y)= elsewhere (a) What is the value of k that renders the above a valid density function? (b) Find the probability that at least 75% of the firms make a profit in the first year. (C) Find the expected proportion of profit and variance of X.
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