Question 1: The CDF of the continuous random variable V is .....v< -5 F, (v) = {(v+ 5)² /144......- 5
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![Question 1: The CDF of the continuous random variable V is
0......
...V< -5
F,(v) = {(v+5)² /144...-5<vs7
..v > 7
1.
а.
What is E[v]?
b. What is Var[v]?
С.
What is E[v?]?](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F5362cbea-9427-4b2b-99cb-57a208edd853%2Ff562556b-f750-49b5-af03-175fa9ecfcbf%2Fwtyk35s_processed.png&w=3840&q=75)
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- Let Y be a discrete random variable with generating function 4 Gy (s) 6 – s s2 What is Var(Y) (in decimal)? Answer:A4. If random variables X and Y each have variance o? = 3 and corr(X,Y) = 0.4, what is the value of Cov(3X – 1, 2Y + 2)?1. The random variables §, §1, §2,... are independent and identically distributed with 1/4 and P(§ = j) = c/j for j = 1,2,3. Let X₁ = 0 and Xn = max(§₁, ..., Èn) for n = 1, 2,.... distribution P(§ = 0) = (a) What value must c take? (b) Explain why {Xn, n = 0, 1, 2,...} is a Markov chain. (c) Write down the transition matrix. (d) Draw the transition diagram and classify the states (aperiodic, transient, re- current, eorgodic, etc). (e) Calculate P(Xn = 0). (f) Calculate P(X₁ = 3, X₂ = 1|X₁ = 3).
- R1(b) Let X₁, X₂, X3 be uncorrelated random variables, having the same variance ². Consider the linear transformations Y₁ = X₁ + X₂, Y₂ = X₁ + X3 and Y3 = X₂ + X3 . Find the correlations of Yi, Y; for i #j. (5 marks)(50) Let X be a random variable with p.d.f. k 1D1. AccountPlease answers the last three questions The random variables ξ, ξ1, ξ2, . . . are independent and identically distributed with distribution P (ξ = 0) = 1/4 and P (ξ = j) = c/j for j = 1, 2, Let X0 = 0 and Xn = max(ξ1, . . . , ξn) for n = 1, 2, . . .. What value must c take? Explain why {Xn, n = 0, 1, 2,..... } is a Markov Write down the transition Draw the transition diagram and classify the states (aperiodic, transient, re- current, eorgodic, etc). Calculate P (Xn = 0). Calculate P (X4 = 3, X2 = 1|X1 = 3).Ex. A lottery ticket with two equally likely outcomes:(1) You win $2 (2) You win $0Let W be the amount won from the lottery. E[W] = 1VAR(W) =???Prove that the events Es, E2... En are independent iff their corresponding indicator variates I,, I₂.. In are independent.Example 2.14. Show the CDF of the random variable X with the following pdf: fx(x) = l0.2(=)O1: Let x be random variable with the following (p.d.f): SC e-* x20 f (x) = 0.W Find: 1. The constant C? 2. The c.d.f? 3. P(1SEE MORE QUESTIONSRecommended textbooks for youA First Course in Probability (10th Edition)ProbabilityISBN:9780134753119Author:Sheldon RossPublisher:PEARSON
A First Course in Probability (10th Edition)ProbabilityISBN:9780134753119Author:Sheldon RossPublisher:PEARSON