Suppose N is a positive integer and γ > 0 a positive real number. For fixed k, calculate the quantity Cγ(k) defined by C (k) := lim N ! γ k 1 − γ N−k.

INSTRUCTIONS TO CANDIDATES

ANSWER ALL QUESTIONS

Homework 

• 1.1 [10 points] What is the probability there are 3 rings between 8:00pm and 8:02pm?

• 1.2 [10 points] What is expected number of rings between 8:00pm and 8:02pm?

• 1.3 [10 points] Given that the bell rang at 9:30pm, what is the probability that the next ring occurs exactly at 9:34pm?

• 1.4 [10 points] Given that the bell rang at 9:30pm, what is the probability that the next ring occurs after 9:34pm?

• 1.5 [10 points] Given that the bell did not ring at all between 9:30pm and 9:34pm, what is the probability that the next ring occurs after 9:37pm?

• 1.6 [10 points] Given that the bell rang 5 times between 9:30pm and 9:34pm, what is the probability that the bell rings 5 times between 10:00pm and 10:02pm?

Q Problem 2 [20 points] Suppose N is a positive integer and γ > 0 a positive real number. For fixed k, calculate the quantity Cγ(k) defined by C (k) := lim N ! γ k 1 − γ N−k.

Q Problem 3 [20 points] Let Y1 and Y2 be independent exponential random variables with respective rates λ1 and λ2. Calculate the probability density function of T = min(Y1, Y2).

Q Bonus [X points] For any random variable Y , the moment generating function of Y is the function of t in R defined by E[etY ]. Calculate the moment generating function of an exponential random variable Y with parameter λ > 0.

Attachments:

Expert's Answer

979 Times Downloaded

Related Questions

. The fundamental operations of create, read, update, and delete (CRUD) in either Python or Java

CS 340 Milestone One Guidelines and Rubric  Overview: For this assignment, you will implement the fundamental operations of create, read, update,

. Develop a program to emulate a purchase transaction at a retail store. This  program will have two classes, a LineItem class and a Transaction class

Retail Transaction Programming Project  Project Requirements:  Develop a program to emulate a purchase transaction at a retail store. This

. The following program contains five errors. Identify the errors and fix them

7COM1028   Secure Systems Programming   Referral Coursework: Secure

. Accepts the following from a user: Item Name Item Quantity Item Price Allows the user to create a file to store the sales receipt contents

Create a GUI program that:Accepts the following from a user:Item NameItem QuantityItem PriceAllows the user to create a file to store the sales receip

. The final project will encompass developing a web service using a software stack and implementing an industry-standard interface. Regardless of whether you choose to pursue application development goals as a pure developer or as a software engineer

CS 340 Final Project Guidelines and Rubric  Overview The final project will encompass developing a web service using a software stack and impleme