2.In each of the cases below, determine if the given functioncould be a probability generating function for a discrete random variable X.If the asnwer is "no", provide a an detailed explanation why, and if the asnweris "yes", justify it, and determine P[X = 3] and P[X = k].a. G(s) = el-sb. G(s) = es-1c. G(s) = 232-$3

Step 1: Definition of a Probability Generating Function (pgf)A probability generating function (pgf)…

Answered: 2. In each of the cases below,…

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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I need help with question #2 please Homework review
Chapters: Normal and Exponential random variables. Q: There exist naturally occurring random variables that are neither discrete nor continuous. Suppose a group of people is waiting for one more person to arrive before starting a meeting. Suppose that the arrival time of the person is exponential with mean 4 minutes, and that the meeting will start either when the person arrives or after 5 minutes, whichever comes first. Let X denote the length of time the group waits before starting the meeting. - a. Find P(0
An ordinary (fair) coin is tossed 3 times. Outcomes are thus triples of "heads" (h) and "tails" (t) which we write hth, ttt, etc. For each outcome, let N be the random variable counting the number of tails in each outcome. For example, if the outcome is tth, then N (tth)=2. Suppose that the random variable X is defined in terms of N as follows: X=N²-2N-2. The values of X are given in the table below. Outcome ttt htt hhh tht tth hth hht thh Value of X 1 -2 -2 -2 -2 -3 -3 -3 Calculate the probabilities P (X=x) of the probability distribution of X. First, fill in the first row with the values of X. Then fill in the appropriate probabilities in the second row. Value X of X P(X=x) 0 0 0 0 0 00 X Ś
Q P.6: On its way, a car meets 4 traffic lights, and the probability that each of them will be red is 0.5. Let X be a discrete random variable equal to the number of traffic lights that were green when the car arrived. X may take the values of 0, 1, 2, 3, 4. (Assume traffic lights are independent.) What is the probability distribution of X? The probability distribution of X is 3 4 p(x) 0.5 0.25 0.125 0.0625 0.0625 The probability of distribution of X is 3 p(x) 0.5 0.5 0.25 0.125 The probability of distribution of X is 3 4 p(x) 0.5 0.25 0.5 0.25 0.125 The probability distribution of X is 1 3 4 p(x) | 0.5 || 0.5 || 0.5 | 0.5 || 0.5 The probability of distribution of X is 3 4 p(x) || 0.0625 0.0625 0.125 0.25 0.5
3. Determine the value c so that each of the following functions can serve as probability distributions of the discrete random variable X: a. f(x) = c(x² +4) for x = 0,1, 2, 3; 3 b. f(x)%3Dс for x= 0,1, 2 3-x
Which of the following is not a property of a discrete probability distribution being valid? All values of P(x) must be positive. All values of P(x) must fall between 0 and 1. All values of x must be positive. The sum of all P(x) values must be 1.
Assume that 12 jurors are randomly selected from a population in which 83% of the people are Asian-Americans. Refer to the probability distribution table below and find the indicated probabilities. xx P(x)P(x) 0 0+ 1 0+ 2 0+ 3 0+ 4 0.0002 5 0.0013 6 0.0073 7 0.0305 8 0.0931 9 0.2021 10 0.296 11 0.2627 12 0.1069 Find the probability of exactly 7 Asian-Americans among 12 jurors.P(x=7)=P(x=7)= Find the probability of 7 or fewer Asian-Americans among 12 jurors.P(x≤7)=P(x≤7)=

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