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(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.

(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.

MATLAB: An Introduction with Applications
MATLAB: An Introduction with Applications
6th Edition
ISBN:9781119256830
Author:Amos Gilat
Publisher:Amos Gilat
Chapter1: Starting With Matlab
Section: Chapter Questions
Problem 1P
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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 ky? ( 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 ky? ( 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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