Problem #2: Let X be a continuous random variable with probability density function 16xe 4x x > 0 o Problem #2(a): Problem #2(b): f(x) = otherwise (a) Find the value of the moment generating function of X at t = 1. (b) Find E[X]. Enter your answer symbolically, as in these examples Enter your answer symbolically, as in these examples
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- S FIU Apply | Florida International Uni.. FIU First Year Applicant | Admission... W UltiPro - UltiPro Login (x- k): 22. Divide by - 6x -16x-5x+9 *-2. -6x-4x+3 R 3 O -6x -4x+ 3 O -6x -4x +3x R 3 -6x -4x +3x None of the above 00:23:07 1 BACK PRE-CALCULUS FORMULA REFERENCE SHEETS DaQuestion 1 1. Suppose you are given that a continuous random variable has a moment generating function of 1 M (t) = 1-3.2t Find the mean and variance of the random variable. mean = var =Question 1 Suppose that X is a random variable with pdf (0 – 1) k-1 fx(k;0) = k=1,2,3,... , 0 > 1 for which E(X)=0 and Var(X)=0(0-1). What is the Cramer-Rao lower bound for a random sample of size n drawn from this pdf? О ө (ө—1) O 0(0 – 1) Ө (ө—1) 1 0 (0 – 1)
- Problem 8: Random variables X and Y have the joint PDF Se, 120, y 2 0, (x² + y) < 1, 1 0, otherwise. Sxx (2, 9) NOTE: "(1? + y)" is not a typo. (a) Find the constat e. (b) Find the marginal PDF fx(x). (c) Find the marginal PDF fr (1). (d) Determine the value of P[X < Y].can you please expand and explainn this problemEvaluate the function for the given values of x. -5 + +7 for x ≤-2 3x+2 4 h(x) = Part 1 of 5 h(-3) = Part 2 of 5 h (3) = Part 3 of 5 h(-2) = for -2Question 2 (a) Prove the following: L{f(t-r)u,(t)}=e**F(s) -ST where, (0 for tpart 3 ,4 and 5Please solve P1Example 7-36. Let {Xx} be mutually independent, each assuming the values 0.12 . ..., a - 1 with probability . Let S, = X1 + X2 + ... + Xp. Show that the probability generatino (6) = {; P (s) : 1- sa a(1 – s) function of S, is : P (S„ = j) = £ (-1)"*j*av (4)(;=u) and hence %3D - av v=01 163Example 17: If P (x) = 0.1 x ,x= 1, 2, 3, 4 = 0 %3D *, otherwise find (i) P{X=1 or 2 } (ii) PRecommended textbooks for youA First Course in Probability (10th Edition)ProbabilityISBN:9780134753119Author:Sheldon RossPublisher:PEARSONA First Course in Probability (10th Edition)ProbabilityISBN:9780134753119Author:Sheldon RossPublisher:PEARSON