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- The 4-dimensional random vector X has PDF fX(x)={1 when 0≤xi≤1, i=1,2,3,4 and 0 otherwise}. Are the for components of X independent random variables?Let X be a random variable with the function, -(x -A) "for x > 2, Let f (x) = { elsewhere. Derive u and show that T = X is biased estimator of 2 . Can you modify T =X in order to get an unbiased estimator of 2.Suppose X is random variable whose p.d.f. is f2)=(2x-x²), 0, OSxs2 Suppose X is random variable whose p.d.f. is f(x)={4 elsewhere Find the mode , if it exists.
- Two random variables X and Y have joint char- acteristic function l@,,m)=exp(-20,?-80;) (i) Show that X and Y are zero mean ran- dom variables.Suppose that one variable, x, is chosen randomly and uniformly from [0, 2], and another variable, y, is also chosen randomly and uniformly from [0, 2]. What is the probability that x ≤ y ≤ 1x + 1? The probability for x ≤ y ≤ 1x + 1 is Round your answer to four decimal places. Submit QuestionThe data of two groups, each group contains two random variables (X1,Y1 and X2,Y2) and each of 30 students is collected. We would like to study the relation between X1,Y1 and X2,Y2 using the measure denoted by T1 andT2, where T1 = E[(Xi – X1)(Yıi – K)]² / [E(x1i - X,)²E(Yu – ¥,)*] ]. T2 = E[(X2i – X2)(Yi – Y)J² / [,E(X2i – X,)² E(Yzi – ¥)²] ]. The data given below, compare between the groups and interpret your results. 1 XI Y1 X2 Y2 98 44 74 52 95 57 79 59 94 66 78 56 81 64 70 74 84 73 79 77 66 65 72 66 73 65 74 50 72 67 98 62 71 66 93 76 67 76 76 84 70 77 86 55 93 66 98 66 92 43 83 65 77 58 68 59 94 56 73 53 76 70 69 74 93 59 90 50 69 59 70 51 86 66 84 55 98 51 78 48 71 64 75 61 95 74 81 53 84 73 73 46 83 69 80 52 78 58 98 61 72 70 79 68 98 53 98 52 73 54 77 56 81 71 84 51 84 49 82 69
- Suppose that X and Y are independent random variables with EX=EY=100, and E[min(X,Y))=79. Find ElX-Y|, (the mean of the absolute value of X-Y).Prove that if M(t) is the MGF of a random variable X, then the MGF of a + bX is e^at M (bt)Let X and Y be two continuous random variables having joint pdffX,Y (x, y) = (1 + XY)/4, −1 ≤x ≤1, −1 ≤y ≤1.Show that X ^2 and Y ^2 are independent.
- If the random variable X follows the uniform distribution U= (0,1) What is the distribution of the random variable Y= -2lnX. Show its limits.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 youLet X ~ N(0, 2) and Y ~ covariances Cov(X,Y) and Cov(Y, X +Y). Exp(A = 3) be two uncorrelated random variables. Find the