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216 CHAPTER 5 MULTIPLE RANDOM VARIA 5.10.3. The random variables X1, ... , Xn have the joint PDF (1 0<xi 31; fx1...
5. Suppose that three random variables Xi, X2, and X3 have a continuous joint distribution with the following p.d.f. (x1+2x2+3z3) and f(1, r2, 3) 0 otherwise. (a) Determine the value of the constant c; (b) Find the marginal joint p.d.f. of Xi and X3; (c) Find P(Xi < 1|X2-2, X3-1)
The joint density of random variables X1, X2 is given by fx1,x2 (x1, 2)= 6x1, for 0 < xı < 1, 0 2 <1 - r Let Y X1X2. Find the joint density of Yi and Y2 Х1, Y?
Exercise 7 (team 5) Let Xi and X2 have joint pdf x1 + x2 if0<x1 < 1 and 0 < x2 < 1 /h.x2 (x1,x2) = 0 otherwise. When Y1 X1X2 derive the marginal pdf for Y.
Consider random variables X and Y with the joint pdf fx1,x2(x1,x2) = 3x1, 0 < x2 < x1 <1. Calculate P(X2 < 1/2 | X1 >= 3/4)
Let λ >0 and suppose that X1,X2,...,Xn be i.i.d. random variables with Xi∼Exp(λ). Find the PDF of X1+···+Xn. Use convolution formula and prove by induction
Please do by hand. Thanks in advance. 5. Let X1 and X2 have joint pdf f(x1, x2) = 4xı, for 0 < x < x2 < l; and 0 otherwise. Find the pdf of Y = X/X2. (Hint: First find the joint pdf of Y and Y2 = X1.)
Observations X1,..., Xn are independent identically distributed, following the PDF fx:(xi) = 0x8-1, and that 0<Xi <1 for all i. The parameter is an unknown positive number. Find the ML estimator of e
5. Let X1, X2, ..., Xn be a random sample from a distribution with pdf of f(x) = (@+1)xº,0<x<1. a. What is the moment estimator for 0 using the method of moments technique? b. What is the MLE for @ ?
5. Let X1, X2,. , Xn be a random sample from a distribution with pdf of f(x) (0+1)x,0< x<1 a. What is the moment estimator for 0 using the method of moments technique? b. What is the MLE for 0?
1. Let X1 and X2 have the joint pdf f(x1, x2) = 2e-11-22, 0 < 11 < 1 2 < 0o, zero elsewhere. Find the joint pdf of Yı = 2X1 and Y2 = X2 – Xı.