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- please helpLet f, g be probability densities such supp(f) c supp(g). show yes X1, ... , Xn X1,..., X, iid. L(g) then f(X;) W; = g(X;) is hopeful 1. Argue why the weights need to be re-normalized even when the normalization constants of the densities f and g are known.Let X be the number of litres of milk shake that is requested at a café on a hot summer day. Assume that ??(??) = 12??(1000−??)21012 , 0<x<1000, zero elsewhere, is the pdf of x. How many litres of milk shake should the store have ready on each of these days, so that the probability of exhausting its supply on a particular day is 0.05?
- 3. Let X; N iid U(0, 1) for i e {1, 2, ...,n}. (a) Compute the pdf of Y; = - log(X;), name the distribution that Y; follows and provide any parameter value or values needed. (b) Compute the pdf that W = [I", X, = X1 X2... X, follows. You may use the result given as part of the Example 2.6 video (even though it will only be proved in Chapter 3). (c) Compute E[W] in the two following ways: (i) through exploiting independence of the X, and using EUV] = E[U]E[V] for any independent random variables U and V. (ii) using the pdf of W computed in the previous part.There are two Gaussian curves below (Plots A and B), along with the respective R source codes.Looking at the plots and the source codes provided, identify the parameters of respective Gaussian pdf's (probability density functions) and the numeric value of x in the PDF F(x)express the areas under the curves in terms of F(x). ( Do not calculate those areas.Your answers must be like F(x) or 1- F(x) for a relevant value of x.) Below is the source code and image for part BSahad prides himself in making a burger in under 4 minutes. The time, Y, in minutes to make the burger can be shown to have the following PDF 금 (y + 2) 01. Let X be an RV with PDF a. Find the mean of X. b. Find the variance of X. f(x) = {¹ -=| - |x| for x < 1 otherwiseState the CLT for independent identically distributed real RVs with mean u and variance a². Suppose that X. X,. . . are independent identically distributed random variables each uniformly distributed over the interval [0, 1]. Calculate the mean and variance of In X. Suppose that 0Let X1,., Xn all be independent exponential distributions all with the same parameter 2. What is the distribution of the minimum of (X1,. a) what is the distribution of the smallest order statistic Y, ? b) Specify both the pdf of the distribution and describe the distribution and its parameters. ,Xn)? In other words:2. Let dt Find the average %3D value of f on the interval [o, 1Show that the characteristic function of a random variable having the binomial density US STIGUIDE.SE is x (@)=[1-p+pelau]NУк. Suppose that Y₁. Y₂; Yn 15. 2 from Function random Sample a population with probability density f(y) = find the maximum BY 1-B B like hood ozy 21: B >0 Elsewhere Estimator of BRecommended textbooks for youMATLAB: An Introduction with ApplicationsStatisticsISBN:9781119256830Author:Amos GilatPublisher:John Wiley & Sons Inc
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