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- An ecologist wishes to mark off circular sampling regions of nearly 10 m in diameter. However the actual diameter of the marked region varies and is a random variable. Let X= actual diameter of a sampled region. The pdf of X is given as |f(x)= k[1-(10-x)^3]; 9let x be a random variable with moment generating function Mx(t)=(0.6 + 0.4e^t)^20 then the variance of x isWith a = .05, the two-tailed critical region for at test using a sample of n = 20 participants would have boundaries of %3D O t-12,136. Ot- +2.080,. Ot--2.093, Ot3 ±2.086.2) Let X be a continuous random variable with PDF 0according to the CDF given below for a random variable Y, plot the pdf and express it mathematically in an accurate manner. b) what is E(Y) ?Q3) Let X1,X2,. X, be a random sample from the truncated exponential distribution with pdf: f(x,0) = Please else (a) Derive the method of moment estimator of 0; (b) Derive the MLE of 0. (c) Are the MOME and the MLE unbiased estimators for 0? (d) Compare the MSE of the MOME and the MLE for 0. Which one is a better estimator for 0Recommended 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,