The joint pmf of the random variables X, Y and Z is given in the table.Y123Z=1X123.001 .002 .003.006.005.004.007 .008a) Determine fx, (2, 2)b) Determine fx-1(2, 2).009Y123Z=21.07.08.09X2.06.05.043.01.02.031Y 23Z = 31.03.02.07X2.01.145.063.05.04.08

Given the joint pmf of the random variables X, Y and Z.

Answered: The joint pmf of the random variables…

MATLAB: An Introduction with Applications

6th Edition

ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

Chapter1: Starting With Matlab

Section: Chapter Questions

Problem 1P

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Suppose that we have a sample space S= {E1 E2, E3, E4, E5, E6' E7}, where E1 E2, ...,E7 denote the sample points.The following probability assignments apply: P(E1)= .05, P(.E2) = .20, P(E3) = .20, P(E4) = .25, P(E5) =.15, P(E6) = .10, and P(E7) = .05. Let A= {E1 E4, E6 } B= {E2 E4, E7 } c= {E2 E3, E6 , E7} a. Find P(A), P(B), and P(C). b. Find A∪ B and P(A ∪ B). c. Find A ∩ B and P(A ∩ B). d. Are events A and C mutually exclusive? e.Find Bc and P(Bc).
A nurse has found that when a patient calls the medical advice line claiming to have the flu, the chance that he or she truly has the flu (and not just a nasty cold) is only about 11%. Of the next 25 patients calling in claiming to have the flu, we are interested in how many actually have the flu. Let the random variable ✗ be the number of patients, out of the 25 who called the medical help line, that actually have the flu. How is X distributed? ✗~B 25 0.11 Find the probability that exactly 9 of the 25 patients actually have the flu. Find the probability that fewer than 8 of the 25 patients actually have the flu. Find the mean of the distribution. Find the standard deviation of the distribution. Part 2 of 2
In the western United States, there are many dry land wheat farms that depend on winter snow and spring rain to produce good crops. About 70% of the years there is enough moisture to produce a good wheat crop, depending on the region. Let r be a random variable that represents the number of good wheat crops in n = 8 years. Suppose the Zimmer farm has reason to believe that at least 4 out of 8 years will be good. However, they need at least 6 good years out of 8 years to survive financially. Compute the probability that the Zimmers will get at least 6 good years out of 8, given what they believe is true; that is, compute P(6 ≤ r | 4 ≤ r). (Round your answer to three decimal places.) Let r be a random variable that represents the number of good wheat crops in n = 10 years. Suppose the Montoya farm has reason to believe that at least 6 out of 10 years will be good. However, they need at least 8 good years out of 10 years to survive financially. Compute the probability that the Montoyas…
Suppoose X and Y are the random variables with joint PMF given by: x\y 11.2 5.75 -3 0 0.07 -2 0.2 0.08 -1 0.1 0.1 0 0.15 0.1 1 0 0.2 a.) Are X and Y independent?
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Exercise 4. Let = {a,b,c,d} and define a probability measure on 222 by P(a) = P(c) = 1/6 and P(b) = P(d) = 1/3. Define random variables X and Y by X(a) = X(b) = 2, X(c) = X(d) = −2 Y(a) = Y(d) = -1, Y(b) = Y(c) = 1. (a) List all sets in σ(Y). (b) Let Z = E(XY), determine Z(a) Z(b), Z(c) and Z(d).
B.202 ul X с Too Weekly w sal Success C X Bb Exam 2 X Bb Take Test: Bb UTF-8 Ass Question Completion Status: nccu.blackboard.com/webapps/assessment/take/launch.jsp?course_assessment_id=_26 http: QUESTION 8 For any continuous random variable, the probability that the random variable takes a value less than zero a. is any number between zero and one. b. is more than one, since it is continuous. c. is a value larger than zero. d. is zero. QUESTION 9 For the standard normal probability distribution, the area to the right of the mean is a. 1. b. 3.09.
Determine E(x) and E(y)
The random variable X takes values -1, 0, 1 with probabilities 1/8, 3/8, 4/8 respectively. a) Write the CDF of X. b) Write the PMF of Y = X² + 2. %3D c) Compute E(Y).
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