Let X have pdf fx(x) = { kr(1-2), 0≤x≤1; 0, otherwise. (a) Determine the distribution function Fx (2), by firstly finding k.
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- 3 Determine whether the following is a valid distribution function F(X) =1-e2 for x2 0 elsewhere5Suppose that a decision maker's risk atitude toward monetary gains or losses x given by the utility function(x) = (50,000+x) 34/2. Suppose that a decision maker has the choice of buying a lottery ticket for $5, or not. Suppose that the lottery winning is $1,000,000, and the chance of winning is one in a thousand. Then..... O The decision maker should not buy the ticket, as the utility from not buying is 223.6, and the expected utility from buying is 223.59. The decision maker should not buy the ticket, as the utility from not buying is 223.6067, and the expected utility from buyingis 223.6065. O The decision maker should buy the ticket, as the utility from not buying 223.60, and the utility from buying is 224.4. The decision maker should buy the ticket, as the utility from not buying 223.6065, and the utility from buying is 223.6067.
- Let P=f(t)=600(1.033)t be the population of a community in year t. Evaluate f(10)Ql: Let f(x) =:1Let X have pdf { [ kr(1-2), 0If X and Y are two independent uniform distribution with X(0 ,4) and Y(0,6). Find the joint pdf f (x.y). Find P(2.5<X<3.5,1<Y<4)a) A university projects that enrollments are going to decline as the pool of college-aged applicants begins to shrink. They have estimated the number of applications for coming years to behave according to the function a = f(t) = 6,500 – 250t where a equals the number of applications for admission to the university and t equals time in years measured from this current year (t = 0). i. What class of function is this? ii. What is the expected number of applications 5 years from today? 10 years? iii. Do you think this function is accurate as a predictor indefinitely into the future? iv. What kinds of factor would influence the restricted domain on t?Suppose that the p.d.f. of X is as given f(x)=4x-1 for 0≤x≤1 and 0 otherwise Find the pdf of Y=X1/2.Assume that X1, X2, X3 ∼ Exp (λ) are independent and evenly distributed with the distribution Exp (λ = 1). (a) Determine the distribution of Y = X1 + X2 + X3 and state its PDF f (y). (b) Determine the distribution of U = 2Y2..You are given fT(30)(t) = t/1250 0≤t<50 0 o.w. a) Find the probability that (30) dies between ages 40 and 45. b) Find the probability that (60) dies between ages 65 and 85. c) Define the cumulative distribution function of T (45). d) Define the force of mortality of T (50).You are given the Posterior pdf fexp[-(0-x)]. p(0|x) = [0, e >x eRecommended 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