Let X - U(1,3) with the following given PDF { ( 0.5, 1
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- Its x-12.5 not exponeIf a single 6-sided die is tossed once, find the probability of rolling a1 The probability is . (Type a whole number or a simplified fraction.)Let 0, X,, X2,... be RVs. Suppose that, conditional on = 0, X1, X2, ... are independent and X, is normally distributed with mean 0 and variance o. Suppose that the marginal PDF of O is 1 T(0) = e 0ER. Calculate the mean and variance of O conditional on X, =x, ..., X,= x„.
- Example 2.17 Let X be a continuous type random variable with PDF given as 1 = (x)f 27 Let Y be another random variable such that Y = X². Find the PDF of Y.IF it was XG (23) Independent of Xen G (13) Find Miley D-Probability density Function of the Variable YaX+Xq 2 -the Mean variance of the variableQ5 If P.d.f of It is given by f(x) = 1 e/sx i) e i) distribution function find iii). (v) P(X>1) 0Compute Var(ys) for the following model, where e; ~ wn(0, 0.01), i.e., a white noise process with mean zero and variance 0.01. 4 = 1+0.5y-1 + et, yo = 1. Please give the exact answer.Each day a random number, N ,of visitors make a purchase. The mean of N is E(N) = 12.8 and its variance is V(N) = 8.5 %3| Each of these visitors independently from the others spends a random amount of money, X; with mean E(X;)= 130.0 and variance V(X;) = 42.0 Let Y Σ Χ a day. be the total amount of money spent by visitors in the shop in Find the mean of Y and the variance of YGiven the pdf: f(x) = { (1/6)e^(1/6x) ; x > 0 0; ew] (i) Find the mean and variance of X using the pdf. (ii) Find the moment generating function of X. (iii) Find the mean and variance of X using the moment generating function.Recommended textbooks for youMATLAB: An Introduction with ApplicationsStatisticsISBN:9781119256830Author:Amos GilatPublisher:John Wiley & Sons Inc
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