X1,, Xn ~ N(-3,2) (random variables) ... Z, = 1(X,X2 + X1X3 + X1X4 + •..+ X1X„), n > 3 %3D (a) Find limn+00EZ,
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- X is an exponential random variable with λ =1 and Y is a uniform random variable defined on (0, 2). If X and Y are independent, find the PDF of Z = X-Y2If X1, X2, ... , Xn constitute a random sample of size n from an exponential population, show that X is a consis-tent estimator of the parameter θ.If the alleles A and B of the cystic fibrosis gene occur in a population with frequencies p and 1 - p (where pis between 0 and 1), then the frequency of heterozygous carriers (carriers with both alleles) is 2p(l - p). Which value of p gives the largest frequency of heterozygous carriers?
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- Consider the data series obtained from a certain experiment for which we have no more information: (0, 1), (0, 2), (2, 2), (3, 4), (4, 6). You want to choose which of two mathematical models best fits the data series. Model 1 is a line y = ax + b, and Model 2 is exponential of the form y = e^(cx). Provide your best approximations for both models, and argue for the reasons for choosing the best model.X1 and X2 are independent random variables such that Xi has PDF fXi(x)={λiexp(−λix) when x≥0, 0 otherwise}. What is P[X2<X1]?Use Bernoulli's method