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An asset manager is compensated daily on the basis of the number of new accounts that are opened with her on that day and the number of existing accounts that she "manages" on each day (for example, she may have to return a phone call from an existing client). Let the number of new accounts opened daily be the random variable N and the number of existing accounts that she manages daily be the random variable E. The probability she'll open exactly N account in a day is given by the pmf PN (N) = 10 = {5.50 0, 5-N N = 1,2,3,4 otherwise Given that she has opened N accounts in a day, the conditional pmf that she'll manage exactly E existing accounts that day is given by the conditional marginal pmf: PEIN(EN) = N 1≤E<5- N 5-A 0, E<1 or E>5-N Her daily salary is based on the formula: S = 2N + E (a) Suppose the manager has opened two new accounts today. What is the conditional probability that she'll manage one, two, or three existing accounts today ("or" in the "exclusive" sense)? (b) Suppose the manager has opened four new accounts today. What is the conditional probability that she'll manage one existing account that day? (c) Derive the joint pmf PN,E (N, E)

An asset manager is compensated daily on the basis of the number of new accounts that are opened with her on that day and the number of existing accounts that she "manages" on each day (for example, she may have to return a phone call from an existing client). Let the number of new accounts opened daily be the random variable N and the number of existing accounts that she manages daily be the random variable E. The probability she'll open exactly N account in a day is given by the pmf PN (N) = 10 = {5.50 0, 5-N N = 1,2,3,4 otherwise Given that she has opened N accounts in a day, the conditional pmf that she'll manage exactly E existing accounts that day is given by the conditional marginal pmf: PEIN(EN) = N 1≤E<5- N 5-A 0, E<1 or E>5-N Her daily salary is based on the formula: S = 2N + E (a) Suppose the manager has opened two new accounts today. What is the conditional probability that she'll manage one, two, or three existing accounts today ("or" in the "exclusive" sense)? (b) Suppose the manager has opened four new accounts today. What is the conditional probability that she'll manage one existing account that day? (c) Derive the joint pmf PN,E (N, E)

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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An asset manager is compensated daily on the basis of the number of new accounts that are opened with her on that day and the number of existing accounts that she "manages" on each day (for example, she may have to return a phone call from an existing client). Let the number of new accounts opened daily be the random variable N and the number of existing accounts that she manages daily be the random variable E. The probability she'll open exactly N account in a day is given by the pmf PN (N) = 5-N N=1,2,3,4 10 0, otherwise Given that she has opened N accounts in a day, the conditional pmf that she'll manage exactly E existing accounts that day is given by the conditional marginal pmf: PEN (EN) = N1≤E≤5-N 0, E<1 or E>5-N Her daily salary is based on the formula: S = 2N + E (a) Suppose the manager has opened two new accounts today. What is the conditional probability that she'll manage one, two, or three existing accounts today ("or" in the "exclusive" sense)? (b) Suppose the manager has opened four new accounts today. What is the conditional probability that she'll manage one existing account that day? (c) Derive the joint pmf PN,E (N, E)
Transcribed Image Text:An asset manager is compensated daily on the basis of the number of new accounts that are opened with her on that day and the number of existing accounts that she "manages" on each day (for example, she may have to return a phone call from an existing client). Let the number of new accounts opened daily be the random variable N and the number of existing accounts that she manages daily be the random variable E. The probability she'll open exactly N account in a day is given by the pmf PN (N) = 5-N N=1,2,3,4 10 0, otherwise Given that she has opened N accounts in a day, the conditional pmf that she'll manage exactly E existing accounts that day is given by the conditional marginal pmf: PEN (EN) = N1≤E≤5-N 0, E<1 or E>5-N Her daily salary is based on the formula: S = 2N + E (a) Suppose the manager has opened two new accounts today. What is the conditional probability that she'll manage one, two, or three existing accounts today ("or" in the "exclusive" sense)? (b) Suppose the manager has opened four new accounts today. What is the conditional probability that she'll manage one existing account that day? (c) Derive the joint pmf PN,E (N, E)
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