Let X and Y be two random variables with the joint pdf as shown in the picture. a. Calculate P (X < 0.4, Y > 0.6) . b. Find the marginal density functions of X and Y. C. Are X and Y independent? Why?
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- Determine if the random variables X and Y are statistically independent or not. NO NEED SOLUTIONSPlease help with this question fast.7.1 Let X be a random variable with probability Si. 1= 1,2, 3, S(2) =10 elsewhere. Find the probability distribution of the random vari- able Y = 2X 1. 7.8 A dealer's profit, in units of $5000, on a new au- tomobile is given by Y = X², where X variable having the density function sa random S(z) =2(1 - 2), 0The Gamma distribution is often used to describe the wait time until a certain number of events occurs. Assume x1, . . . , xn ∼iid Gamma(α, β), where α is shape and β is rate. Calculate the maximum likelihood estimator of β either by hand or via R, but not both. The probability density function (PDF) for the Gamma distribution is: Calculate the log-likelihood function of the function below. I t doesnt have to be on r studi you can do by your handCont?I need help with thisThe density function of X random variable is given below; check image.Let Y denote a random variable with the following density function. 1 f (y) = { In(2)(+1) if 0he length of time, in minutes, for an airplane to obtain clearance for takeoff at a certain airport is a random variable Y = 3X-2, where X has the density function. Find the mean and variance of the random variable Y.Let X and Y be two independent random variables with PDFS fy (x) = 1536 x4 with x> 8 and fy(y)= 25 Y with 0Assume that x,, . .. , Xn are the realization of the random samples X, ... , Xn with pdf or pmf fo. Find the UMP of Ho : 0 = 0 versus H, : 0 = 0, . for 0, > 0o fe(x) is density of normal with mean 0 and known o. fe(x) is density of normal with known mean u and variance 0 = o² .2.5 Y has a density function S0) = (2 y), 0 < y < 2 elsewhere Find the mean and variance of Y.Recommended textbooks for youMATLAB: An Introduction with ApplicationsStatisticsISBN:9781119256830Author:Amos GilatPublisher:John Wiley & Sons Inc
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