Consider three independent Poisson random variables X, Y, and Z with parameters λ₁ = 1, λ₂ = 1, and λ3 = 9,respectively.What is the probability that X, Y, and Z are all equal? Express your answer as a infinite sumof exponentials and factorials.Consider a new random variable D = Z - X? Is D distributed as a Poisson? Explain yourConsider two new random variables S = X + Z and T = Y + Z? What is p(S, T)?Intuitively, explain why p(S, T) approaches 1.0 as you increase the value of 13 while leavingthe values of ₁ and 2 unchanged?

Solution: As per the guidelines first three sub-parts should be answered. In case the remaining…

Answered: Consider three independent Poisson…

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...

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b. Let X1, X2, X3, and X4 represent the weight of shipment packages at a certain shipment facility. Suppose they are independent normal random variables with means H1 = 3.6, 42=0.9, 3= 1.8, 4 = 7.4 pounds and variances o = = = Find P (2X₁ + 1X2 + 3X3 + 1X4 ≤ 17.6). = 1.
Let a be a random variable representing the percentage of protein content for early bloom alfalfa hay. The average percentage protein content of such early bloom alfalfa should be u = 17.2%. A farmer's co-op is thinking of buying a large amount of baled hay but suspects that the hay is from a later summer cutting with lower protein content. A small amount of hay was removed from each bale of a random sample of 50 bales. The average protein content from the samples was determined by a local agricultural college to be -15.8% with a sample standard deviation of S = 5.3%- At a = .05, does this hay have lower average protein content than the early bloom alfalfa?
You currently work for the DARPA, the Defense Advanced Research Projects Agency. You've received reports of some strange things occurring in the small town of Hawkins, Indiana. Let U be a random variable equal to 1 if the citizen has been to the Upside Down and 0 otherwise. Let S be a random variable equal to 1 if a citizen reports being in the presence of a group of misfit kids who claim to be "saving the town" and 0 otherwise The table below shows the joint probability density function for the galactic population Share of Population 0.15 0.32 0.50 0.03 U 0 0 1 1 S 1 0 1 0 Round to 2 decimal places where necessary, unless otherwise stated. Leave your answer in decimals, rather than convert to percentages. A. Evaluate Fu,s (1,0): B. Calculate the share of people who have been to the Upside Down in the population. That is, E(U): C. Calculate the probability of having gone to the Upside Down conditional on meeting this band of misfit kids?. That is, Fus (11):
Consider a discrete random variable X that can assume three values 1, 2, and k with respective probabilities 0.5, 0.25, and 0.3. If E(X) = 1.9, what is the value of k? Select one: а. 5 b. 2 с. 1 d. 3 e. 4

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