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22. An instructor in a technical writing class has asked that a certain report be turned in the following week, adding the restriction that any report exceeding for pages will not be accepted. Let Y the number of pages in a randomly chosen student's report and suppose that Y has probability mass function y | 1 | 2 | 3 | 4 P(Y = y) | 0.001 | 0.19 | 0.35 | 0.45 a) Compute E(Y). b) Compute Var(Y). c) Suppose the instructor spends ?Y minutes grading a paper consisting of Y pages. What is the expected amount of time, E(?Y) , spent grading a randomly selected paper? 23. For what values of the constant c are the following functions of probability density functions? a) f_X(x) = { ce^-6x, x > 0; -cx, -1 < x ? 0; 0, x ? -1 b) f_X(x) = { cx^2e^-x^3, 0 < x < ?; 0, elsewhere 24. A computer producing factory has only two plants T1 and T2. Plant T1 produces 20% and plant T2 produces 80% of the total computers produced. 7% of computers produced in the factory turn out to be defective. It is known that P(computer turns out to be defective, given that it is produced in plant T1) = p1, P(computer turns out to be defective, given that it is produced in plant T2) = p2 such that p1 = 10p2, where P(A) denotes the probability of an event A ? ? (sample space). A computer produced in the factory is randomly selected and it does not turn out to be defective. Then, what is the probability that it is produced in plant T2? 25. Suppose that the amount of time one spends in a bank is exponentially distributed with mean 10 minutes. What is the probability that a customer will spend more than 15 minutes in the bank? What is the probability that a customer will spend more than 15 minutes in the bank given that he is still in the bank after 10 minutes?

          22. An instructor in a technical writing class has asked that a certain report be turned in the following week, adding the restriction that any report exceeding for pages will not be accepted. Let Y the number of pages in a randomly chosen student's report and suppose that Y has probability mass function

y | 1 | 2 | 3 | 4
P(Y = y) | 0.001 | 0.19 | 0.35 | 0.45

a) Compute E(Y).
b) Compute Var(Y).
c) Suppose the instructor spends ?Y minutes grading a paper consisting of Y pages. What is the expected amount of time, E(?Y) , spent grading a randomly selected paper?

23. For what values of the constant c are the following functions of probability density functions?
a) f_X(x) = { ce^-6x, x > 0; -cx, -1 < x ? 0; 0, x ? -1
b) f_X(x) = { cx^2e^-x^3, 0 < x < ?; 0, elsewhere

24. A computer producing factory has only two plants T1 and T2. Plant T1 produces 20% and plant T2 produces 80% of the total computers produced. 7% of computers produced in the factory turn out to be defective. It is known that P(computer turns out to be defective, given that it is produced in plant T1) = p1, P(computer turns out to be defective, given that it is produced in plant T2) = p2 such that p1 = 10p2, where P(A) denotes the probability of an event A ? ? (sample space). A computer produced in the factory is randomly selected and it does not turn out to be defective. Then, what is the probability that it is produced in plant T2?

25. Suppose that the amount of time one spends in a bank is exponentially distributed with mean 10 minutes. What is the probability that a customer will spend more than 15 minutes in the bank? What is the probability that a customer will spend more than 15 minutes in the bank given that he is still in the bank after 10 minutes?

22. An instructor in a technical writing class has asked that a certain report be turned in the following week, adding the restriction that any report exceeding for pages will not be accepted. Let Y the number of pages in a randomly chosen student's report and suppose that Y has probability mass function

y | 1 | 2 | 3 | 4
P(Y = y) | 0.001 | 0.19 | 0.35 | 0.45

a) Compute E(Y).
b) Compute Var(Y).
c) Suppose the instructor spends ?Y minutes grading a paper consisting of Y pages. What is the expected amount of time, E(?Y) , spent grading a randomly selected paper?

23. For what values of the constant c are the following functions of probability density functions?
a) fX(x) = ce^-6x, x > 0; -cx, -1 < x ? 0; 0, x ? -1
b) fX(x) = cx^2e^-x^3, 0 < x < ?; 0, elsewhere

24. A computer producing factory has only two plants T1 and T2. Plant T1 produces 20% and plant T2 produces 80% of the total computers produced. 7% of computers produced in the factory turn out to be defective. It is known that P(computer turns out to be defective, given that it is produced in plant T1) = p1, P(computer turns out to be defective, given that it is produced in plant T2) = p2 such that p1 = 10p2, where P(A) denotes the probability of an event A ? ? (sample space). A computer produced in the factory is randomly selected and it does not turn out to be defective. Then, what is the probability that it is produced in plant T2?

25. Suppose that the amount of time one spends in a bank is exponentially distributed with mean 10 minutes. What is the probability that a customer will spend more than 15 minutes in the bank? What is the probability that a customer will spend more than 15 minutes in the bank given that he is still in the bank after 10 minutes?

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