Let X1, ... , Xn be a random sample have the pdf 1 (1-0) f(x,0) = -(x),0 < x < 1, 0<0 < ∞. Find mle of 0.
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- a. What is the joint marginal PDF of X and Z?b. What is [P 0 <= Y <= 3/2 | X = 1/3 Z = 5/2]?Let X1, X2 denote two independent variables, each with a x^2(2) distribution. Find the joint pdf of Y1=X1 and Y2 = X2+X1. Note that the support of Y1, Y2 is 0<y1<y2<infinity. Also, find the marginal pdf of wach Y1 and Y2. Are Y1 and Y2 independent?