1 Suppose that X is a continuous random variable with the density functions f(x) =a n2) for 1sx s2. Xisalso jointiy distributed with the continuous random variabieY, and the conditional density function of Y given X is fyx=x)=x-etor ISxs2 and y>0. Find the marginal density Tunction ofY.
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- A continuous variable Y has a probability density function for which the moment generating function is given by M(t)=e^(2*t+72*t^2). What is the variance of the variable, Var[Y]?Let X and Y be two independent continuous random variables with the following probability density functions: f(x) = (1/2)e^(-x/2) for x > 0 g(y) = (1/3)e^(-y/3) for y > 0 What is the probability density function of Z = X + Y?The density of a random variable X is f(x) = C/x^2 when x ≥ 10 and 0 otherwise. Find P(X > 20).
- Let X and Y be two independent random variables with densities fX(x) = e^(-x), for x>0 and fY(y) = e^y, for y<0, respectively. Determine the density of X+Y.Suppose that two continuous random variables X and Y have joint probability density function fxy = 1sxs2,0sy<3 elsewhere Find the strength of the relationship and interpret the findings.let x denotes the percentage of time out of 40 hour workweek that a call center agent is serving a client by answering phone calls, suppose that x has probability density function defin by f(x)=3x^2 for 0< x < 1. find the mean and variance of x
- Let X be a continuous random variable with density functionf(x) = 3x^-4, x ≥ 1. Compute E(X ) and Var(X ).Let X ~ Uniform(a, b). Find Expected value EX.The joint probability density function of two dimensional random variable(X,Y) is given 8 by f(x, y) = xy, 13xsys2 9 = 0, elsewhere Find the marginal density functions of X and Y.
- Actuary Tong has to study for two actuarial exams: Exam P and Exam FM. The amount of study time that Actuary Tong will spend on each exam in a day follows a continuous random variable that ranges from o to i hour. The amount of study time that Actuary Tong spends on both exams in a day has a joint density function that is equal to the sum of the study times that Actuary Tong spends on ench exam in a day. Caleulate the probability Actuary Tong spends at least half an hour in a day studying for exactly one of the exams. A 0.45 B 0.50 0.55 D 0.60 0.65 REPQ2) The shelf life, in days, for bottles of a certain prescribed medicine is a random variable having the density function as shown below, Find the probability that a bottle of this medicine will have a shelf life of anywhere between 40 and 120 days 20000 0The density function, ху fy(x, y) = f(x) =9 0, 0SEE MORE QUESTIONSRecommended textbooks for youMATLAB: An Introduction with ApplicationsStatisticsISBN:9781119256830Author:Amos GilatPublisher:John Wiley & Sons Inc
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