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is binomia triáls and parameter (a) Determine E(Y | X = x) and V(Y |X = x). (b) Use the previous part and the laws of total expectation and variance to find E(Y) and V(Y) (c) Show that Y also has a Poisson distribution. Find its parameter and verify your answer to the previous item that way.

is binomia triáls and parameter (a) Determine E(Y | X = x) and V(Y |X = x). (b) Use the previous part and the laws of total expectation and variance to find E(Y) and V(Y) (c) Show that Y also has a Poisson distribution. Find its parameter and verify your answer to the previous item that way.

Calculus For The Life Sciences
Calculus For The Life Sciences
2nd Edition
ISBN:9780321964038
Author:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.
Publisher:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.
Chapter13: Probability And Calculus
Section13.CR: Chapter 13 Review
Problem 6CR
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M-4 please help me with the below problem with step by step explanation clearly.

Needed all parts clearly, please.

4. The number X of calls coming into Campus Safety follows a Poisson distribution with parameter 1 = 5. The probability that any particular call is a prank call is 0.2, independent of any other call. Let Y be the number of prank calls received. This means that, given a value r for X, the variable Y is binomial with r trials and parameter 0.2. (a) Determine E(Y |X = x) and V(Y | X = x). (b) Use the previous part and the laws of total expectation and variance to find E(Y) and V(Y) (c) Show that Y also has a Poisson distribution. Find its parameter and verify your answer to the previous item that way.
Transcribed Image Text:4. The number X of calls coming into Campus Safety follows a Poisson distribution with parameter 1 = 5. The probability that any particular call is a prank call is 0.2, independent of any other call. Let Y be the number of prank calls received. This means that, given a value r for X, the variable Y is binomial with r trials and parameter 0.2. (a) Determine E(Y |X = x) and V(Y | X = x). (b) Use the previous part and the laws of total expectation and variance to find E(Y) and V(Y) (c) Show that Y also has a Poisson distribution. Find its parameter and verify your answer to the previous item that way.
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