4. Let X have pdf f(c) as follows . (8 pts) What is EX]? Justify your...
4. Let X have pdf (a) as follows 1) 1/2) + .2 1(1/2 < x f(z) = 1.81(0 x (8 pts) What is E[Xj? Justify your answer. (12 pts) Write Matlab or pseudocode that will produce 10, 000 PRNG samples with the dis- tribution of X. Have the output recorded in the vector a (i.e., so that (1) is the first sample, (2) is the second sample, etc.)
4. Let X have pdf (a) as follows 1) 1/2) + .2...
4. Let X have pdf f (x) as follows f(x) = 1.8 1(0 1/21+ .21(1/2 < x 1) x (8 pts) What is E[X]? Justify your answer. . (12 pts) Write Matlab or pseudocode that will produce 10, 000 PRNG samples with the dis- tribution of X. Have the output recorded in the vector a (i.e., so that ar(1) is the first sample, r(2) is the second sample, etc.)
4. Let X have pdf f (x) as follows f(x) =...
2.22 Let X have the pdf (a) Verify that f(z) is a pdf. (b) Find EX and Var X.
8. (10 Pts) Answer by True / False and justify your answer. (a) Let A be a 2 × 2 matrix such that(A2-Nthen, if A ±1 A--. (b) If C is a skew-symmetric matrix of odd order n, then |C-0 (c) If A is a square matrix, and the linear transformation L(z) Az is one-to-one, then the linear transformation x ? At is also one-toone. z), ? O (z, y, z) = (az, ay, 0), then V is not a...
Let the random variables x and y have joint pdf as follows: 4 x < 1,0< y< 3 0 3 2) (round off to third decimal place). Find P(X>
(25 pts.) Let the random variable X have pdf f(x) = { 0<x<1 1<isa Generate a random variable from f(x) using (a) The inverse-transform method (b) The accept-reject method, using the proposal density 9(x) = 0sos
4. (30 pts) Let (X,Y) have joint pdf given by e-y, 0 < x < y < 0, f(x,y) = { | 0, 0.w., (a) Find the correlation coefficient px,y. (20 pts) (b) Are X and Y independent? Explain why. (10 pts)
4. (30 pts) Let (X,Y) have joint pdf given by < , | e-9, 0 < x < f(x,y) = 3 | 0, 0.w., (a) Find the correlation coefficient px,y: (20 pts) (b) Are X and Y independent? Explain why. (10 pts)
3. (50 pts) Let (X,Y) have joint pdf given by -{ c, lyl< x, 0 < x < 1, f(x,y) = 0, 0.w., (a) Find the constant c. (b) Find fx(x) and fy(y) (c) For 0< x<1, find fy x-() and pyix- and ox (d) Find Cov(X, Y) (e) Are X and Y independent? Explain why
3. (50 pts) Let (X, Y) have joint pdf given by c, y x, 0 < x < 1, f(x, y) 0, o.w., (a) Find the constant c. (b) Find fx(x) and fy (y) (c) For 0 < 1, find fyx=x(y) and pyjx=x and oy Y|X=x (d) Find Cov(X, Y) (e) Are X and Y independent? Explain why.