4. 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 pdf that characterizes the proportion Y that make a profit is given by ſky*(1 – y)³, 0

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4. 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 pdf that characterizes the
proportion Y that make a profit is given by
Sky*(1 – y)³, 0 <y<1
elsewhere
f(y) =
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.
Transcribed Image Text:4. 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 pdf that characterizes the proportion Y that make a profit is given by Sky*(1 – y)³, 0 <y<1 elsewhere f(y) = 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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