3.33 Suppose a certain type of small data processingfirm is so specialized that some have difficulty makinga profit in their first year of operation. The probabil-ity density function that characterizes the proportionY that make a profit is given bySky²(1-y)³, 0 ≤ y ≤1,f(y) =10,elsewhere.(a) What is the value of k that renders the above avalid density function?(b) Find the probability that at most 31% of the firmsmake a profit in the first year.(c) Find the probability that at least 74% of the firmsmake a profit in the first year.

The provided information is as follows:The probability density function is given as

Answered: 3.33 Suppose a certain type of small…

A First Course in Probability (10th Edition)

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Chapter1: Combinatorial Analysis

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3.33 Suppose a certain type of small data processing firm is so specialized that some have difficulty making a profit in their first year of operation. The probabil- ity density function that characterizes the proportion Y that make a profit is given by 3 Sky³ (1-y)² 0≤ y ≤ 1, f(y) = 0, elsewhere. (a) What is the value of k that renders the above a valid density function? (b) Find the probability that at most 50% of the firms make a profit in the first year. (c) Find the probability that at least 80% of the firms make a profit in the first year.
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