Suppose that Z is a discrete random variable with positive expectation. If Var(Z) = 3 and E(Z²) = 4, match upthe following quantities.Var(2Z)Var(Z² – 5)E(1-4Z)E(Z² - 5)Var(2 - Z)Drag answer hereDrag answer hereDrag answer hereDrag answer hereDrag answer here-312Cannot be determined3-1

Answered: Image /qna-images/answer/c31c31de-c01a-4e30-aaf6-b0314dcf43cc.jpg

Answered: Suppose that Z is a discrete random…

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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: Let X and Y be independent random variables such that with a prob. 1/3 with a prob. 2/3 with a prob. 3/4 with a prob. 1/4 X = 1 = 0 %3D and Y = 2 =- 3 Find (c) E (XY)
Let Y be a discrete random variable with generating function 4 Gy (s) 6 - s What is E(Y) (in decimal)? Answer:
Let Y be a discrete random variable with generating function 4 Gy (s) 6 – s s2 What is Var(Y) (in decimal)? Answer:
B5. Let X₁, X₂, ..., Xn be IID random variable with common expectation µ and common variance o², and let X = (X₁ + + X₂)/n be the mean of these random variables. We will be considering the random variable S² given by (a) By writing or otherwise, show that S² (b) Hence or otherwise, show that n S² = (x₁ - x)². = Ĺ(X₂ i=1 X₁ X = (X₁-μ) - (x-μ) = Σ(X; -μ)² - n(X - μ)². i=1 ES² = (n-1)0². You may use facts about X from the notes provided you state them clearly. (You may find it helpful to recognise some expectations as definitional formulas for variances, where appropriate.) (c) At the beginning of this module, we defined the sample variance of the values x₁, x2,...,xn to be S = 1 n-1 n i=1 ((x₁ - x)². Explain one reason why we might consider it appropriate to use 1/(n-1) as the factor at the beginning of this expression, rather than simply 1/n. B6. (New) Roughly how many times should I toss a coin for there to be a 95% chance that between 49% and 510/ of my nain toon land Honda?
A Gaussian random variable has a PDF of the form √ fx(x) = (a) Pr(X>0), (c) Pr(X 3), (g) Pr(X+2] > 1), NT exp(-2(x + 1)²). Write each of the following probabilities in terms of Q-functions (with positive arguments) and also give numerical evaluations: (b) Pr(X>2) (d) Pr(X<-4), (f) Pr(|X+1 <2) (h) Pr(X-1<2)
Suppose that Z is a discrete random variable with positive expectation. If Var(Z) = 3 and E(Z²) = 4, match up the following quantities. E(1 - 4Z) Drag answer here E(Z² - 5) Drag answer here Var(Z² – 5) Drag answer here Var(2Z) Drag answer here Var(2 - Z) Drag answer here 3 Cannot be determine d 12 -1 -3
Complete the following multiple choice questions. No work will be graded in the bonus problem. (a) E(X²)= 16. Compute E[-X(3X – 2)]. Assume that X is a random variable with E(X)= -3 and | (i) -54 (ii) -48 (iii) -33 (iv) -27
Answer no. 1 only
Can you please do this problem step by step and can you label which one is mean, variance and pmf of X
(1) Let X be a random variable with a function k(3x2 +6) f(x) =- -1,0,1,2 then O.w 1 1 1 (a) k = 44 (b) k =- 43 7 (c) k = 42 (d) k (e) None of these 44 a is the correct answer b is the correct answer O c is the correct answer d is the correct answer e is the correct answer
Assume that McDonalds can serve a customer's order in X minutes after the customer enters the fast food chain. The PDF of the random variable X is shown as: 0.1 10 Moreover, assume that the customer can finish the food Y minutes after it is served, independent of the serving time. The PDF of the random variable Y is shown as: i. ii. |fx(x) 0.1 fy(y) fy(y) = 0.1e-0.1y 50 Let Z = X + Y be the total amount of time that the customer stays inside the fast food chain. 15 20 What is the probability that the customer stays within McDonalds for at most 18 minutes, i.e. P(Z < 18)? What is the expected value (in minutes) that the customer stays within the fast food chain?

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