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)

10th Edition

ISBN:9780134753119

Author:Sheldon Ross

Publisher:Sheldon Ross

Chapter1: Combinatorial Analysis

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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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2. In probability, it is common to model the deviation of a day's temperature from the monthly average temperature using the Gaussian probability density function, 1.-/9 f(t) = V9T This means that the probability that the day's temperature will be between t = a and t = b different from the monthly average temperature is given by the area under the graph of y = f(t) between t a andt = b. A related function is %3D F(x) = -2/9 dt, 2 0. %3D V9n Jo This function gives the probability that the day's temperature is between t = -x and t = x different from the monthly average temperature. For example, F(1) 0.36 indicates that there's roughly a 36% chance that the day's temperature will be within 1 degree (between 1 degree less and 1 degree more) of the monthly average. 1 (a) Find a power series representation of F(x) (write down the power series using sigma notation). (b) Use your answer to (a) to find a series equal to the probability that the day's temperature will be within 2 degrees of the…
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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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A college professor never finishes his lecture before the end of the hour and always finishes his lectures within 2 min after the hour. Let X = the time that elapses between the end of the hour and the end of the lecture and suppose the pdf of X is as follows. 0 ≤ x ≤ 2 f(x) = {kx² otherwise (a) Find the value of k. (Enter your answer to three decimal places.) Draw the corresponding density curve. [Hint: Total area under the graph of f(x) is 1.] f(x) f(x) 1.5 O 1.0 0.5 f(x) 1.5 1.0 0.5 X 0.5 1.0 1.5 2.0 X 0.5 1.0 1.5 2.0 1.5 1.0 0.5 f(x) 1.5 1.0 0.5 X 0.5 1.0 1.5 2.0 X 0.5 1.0 1.5 2.0 (b) What is the probability that the lecture ends within 1 min of the end of the hour? (Enter your answer to three decimal places.) (c) What is the probability that the lecture continues beyond the hour for between 15 and 60 sec? (Round your answer to four decimal places.) (d) What is the probability that the lecture continues for at least 75 sec beyond the end of the hour? (Round your answer to four…
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