Let X1,...,X, be independent random variables with pdfs f(z:(0) = { 0 -i(0 – 1) < z; < i(@ + 1) otherwise, where 0 > 0. Find a two-dimensional sufficient statistic for 0.
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- Q3/A/ Let X be a r.v with p.d.f f(x) = e-lkl - oFind the mean of the random variable X with PDF S 3x² _if 0Find the variance of the random variable X with a PDF given by 3x2 S* if - 1< x< 1, f(x) = 2 otherwise. Submit your answer in fractional form.An ordinary (fair) coin is tossed 3 times. Outcomes are thus triple of “heads” (h) and tails (t) which we write hth, ttt, etc. For each outcome, let R be the random variable counting the number of tails in each outcome. For example, if the outcome is hht, then R (hht)=1. Suppose that the random variable X is defined in terms of R as follows X=6R-2R^2-1. The values of X are given in the table below. A) Calculate the values of the probability distribution function of X, i.e. the function Px. First, fill in the first row with the values X. Then fill in the appropriate probability in the second row.Y, = XB + ɛ, Show that the model variance in model Yi unbiased estimator ofShow that variance o? = (x²) – ((x))²calculate the variance of g(X) =X^2+2, where X is the random variable with probability distribution : x=0,1,2,3; f(x) = 0.1, 0.2, 0.4,0.3 . a. 19.65 b. 26.28 c. 10.65 d. 11.65 e. 14.65Suppose that f(x) = 0.125x for 0 < x < 4 Determine the mean and the variance of X.Suppose that f (x) = 0.125x for 0 < x < 4 Determine the mean and the variance of X.Suppose that the random change in value of a financial asset is X over the first day and Y over the second. Suppose also that Var(X) =18 and Var(Y) = 26 In this case, the total change in the value over these two days is given by X +Y. Do you have enough information to compute Var(X +Y)? If so, compute this value. If not, explain what additional information you need to do so.the random variable Y is such that : E(2Y+3)=6 and Var(2-3Y)=11 find E(Y^2)Let X and Y are 2 independent random variables N (0,1) Questions: how to find E(X), E(Y), E(X^2), E(Y^2)? Thank youSEE MORE QUESTIONSRecommended textbooks for youCalculus For The Life SciencesCalculusISBN:9780321964038Author:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.Publisher:Pearson Addison Wesley,Calculus For The Life SciencesCalculusISBN:9780321964038Author:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.Publisher:Pearson Addison Wesley,