3. [10 pts.] Suppose r.v. y is uniformly distributed over (0,27) i.e. f*() = 1/2, for...
5. Let X be uniformly distributed in [0, 1]. Given X = x, the r.v. Y is uniformly distributed in 0, x for 0<x<1 (a) Specify the joint pdf fxy(x,y) and sketch its region of support Ω XY. (b) Determine fxly(x1025). (c) Determine the probability P(X〈2Y). (d) Determine the probability P(X +Y 1)
5. Let X be uniformly distributed in [0, 1]. Given X = x, the r.v. Y is uniformly distributed in 0, x for 0
Need help with question 2 (not question 1) 1. Suppose that (X,Y) is uniformly distributed over the region {(x, y): 0 < \y< x < 1}. Find: a) the joint density of (X, Y); b) the marginal densities fx(x) and fy(y). c) Are X and Y independent? d) Find E(X) and E(Y). 2. Repeat Exercise 1 for (X,Y) with uniform distribution over {(x, y): 0 < \x]+\y< 1}.
10. Suppose (X, Y) is uniformly distributed over the disk 2 + y 36. Then 10. Suppose (X, Y) is uniformly distributed over the disk 2 + y 36. Then
Suppose that Y=cos(X), where X is uniformly distributed over the interval [0, 2Pi]. Determine the pdf of the random variable Y.
2. Suppose a r.v. X has the density function 2 x, for 0<x<1 f(x) = 10, otherwise Observe X independently for three times, let y denote the number of an event {X<0.5) occurring in three times. (1) What is the probability of the event {X<0.5}? (2) What is the probability distribution of Y ? Write out its probability mass function
Let X,Y be uniformly distributed in the rectangle defined by −3 < x−y < 3, 1 < x + y < 5. Find the marginal density fX(x) and E(Y|X).In the same situation find Cov(X,Y ). (3) Let X, Y be uniformly distributed in the rectangle defined by -3 < x-y<3, Find the marginal density fx(x) and E(Y|X). In the same situation find Cov(X, Y). 1<x+y<5.
Suppose F(t) /6 for 0 < t < 6 is the c.df. Y. If Y is a continuous-type r.v., give the p.d.f. of Y. If Y is a discrete-type r.v., give the p.m.f. of Y. Otherwise, say that Y is none of the above. of a randorm variable
Let X be a continuous random variable uniformly distributed on the unit interval (0, 1), .e X has a density f(x) = { 1, 0<r<1 f (x)- 0, elsewhere μ+ơX, where-oo < μ < 00, σ > 0 (a) Find the density of Y (b) Find E(Y) and V(Y)
6-x-4, 0x<2 0 1 2cych Exri If for two R.V. s X&Y the joint pdf is given by, otherwise Find Frix (o (1), Frix (alt), Ely/x-1]. var [Ylx-i] = E[^\x-]- (E[1\x=1])!