Let X and Y be two discrete random variables. We define Z = X + Y , i.e. Vw E Q, Z(@) = X(@) + Y(@). i) Show that: P(Z = z) = _fx,v(x, z – x) - Z ii) Now assume that X and Y are independent. Show that: P(Z = 2) = ) fx(x)fr(z-x) = ) fx(z-y)fv(y) From now on, we assume that X and Y are independent random variables which have the Poisson distributions with parameters Ax and Ay, respectively. iii) Show that Z has the Poisson distribution, with parameter Ax + Ay. iv) Show that the conditional distribution of X, given X + Y = n, is binomial, and find its parameters.

Let X and Y be two discrete random variables. We define Z = X + Y , i.e. Vw E Q, Z(@) = X(@) + Y(@). i) Show that: P(Z = z) = _fx,v(x, z – x) - Z ii) Now assume that X and Y are independent. Show that: P(Z = 2) = ) fx(x)fr(z-x) = ) fx(z-y)fv(y) From now on, we assume that X and Y are independent random variables which have the Poisson distributions with parameters Ax and Ay, respectively. iii) Show that Z has the Poisson distribution, with parameter Ax + Ay. iv) Show that the conditional distribution of X, given X + Y = n, is binomial, and find its parameters.

A First Course in Probability (10th Edition)

10th Edition

ISBN:9780134753119

Author:Sheldon Ross

Publisher:Sheldon Ross

Chapter1: Combinatorial Analysis

Section: Chapter Questions

Problem 1.1P: a. How many different 7-place license plates are possible if the first 2 places are for letters and...

See similar textbooks

Similar questions

Please solve subparts A,B and no reject. Because its no essay thank u Question This study aims to determine the need for SPKLU (public electric vehicle charging stations) or charging stations (CS) for owners of battery-based electric motorized vehicles (KBLBB) in Indonesia. Data for the year until the end of 2021 recorded as many as 800 KBLBB from various brands (Hyundai 700, BYD 24, Tesla 56, Nissan 20). There is a list of names of KBLBB owners according to the brand. It is suspected that the need for SPKLU differs according to the brand of the car. A. If the sample will be selected as many as 80 KBLBB owners. Determine the sampling technique that is in accordance with the population information above. And write down the steps / stages until 80 people are selected (choose 80 people out of 800 people) B. Explain the difference between random and non-random sampling techniques. And explain the sampling technique in each of these sampling techniques (randon and non-random)
Please help with parts c, d, and e. Thank you!
Find volume
Use the dot method to add the numbers below. If the number needs a dot, put a dot (period) to the right of the number. Otherwise leave it blank.
Simplify attached image.