Is it generally true that if the support of (X, Y) is a triangle, then X and Y are dependent random variables?
Is it generally true that if the support of (X, Y) is a triangle, then X...
(3) A pair of random variables (X, Y) is distributed uniformly on the triangle with vertices (0,0), (2,0) and (0. Find EX, EY, Cov(X,Y), E(max{X,Y)), P(X> Y), P(X 2 Y)
3. The pair of random variables X and Y is uniformly distributed on the interior of the triangle with the vertices whose coordinates are (0,0), (0,2), and (2,0) (i.e., the joint density is equal to a constant inside the triangle and zero outside). (a) (10 points) Find P(Y+X< 1). (b) (10 points) Find P(X = Y). (c) (10 points) Find P(Y > 1X = 1/2). 3. The pair of random variables X and Y is uniformly distributed on the interior...
True or False (a) If X ∩ Y = ∅ then the two events X and Y are independent? (b) If event X is independent of event Y, then X^c is independent of Y? (c) For a discrete random variable X, we have limx->∞ pX(x) = 0? (d) For a continuous random variable X, we have limx->∞ fX(x) = 0? (e) For a continuous random variable X, we have limx->0 fX(x) ≤ 1? (f) For two discrete random variables X...
Is E(X/Y)=E(X)/E(Y) true for all independent random variables X and Y provided Y ≠ 0 and E(Y) ≠ 0? - yes - no Please explain
Let X and Y be two dependent random variables. P[X,Y]= 0.2 and P[X] =0.4. Find P[Y|X].
True or False With explanation please. 1- True or falso: a. The expectation of a random variable uniformly distributed over (a, b) is equal to (6-a) b. If the random variable X is applied to the input of a Half-wave rectifier, So the output is x>0, xs0., th cterized as r=g(X): g(x)-10. x, en - X) If a and b are constants and X is a random variable and Y-aX+b, then f v) d. If a and b are constants...
Suppose three random variables X, Y, Z have a joint distribution PX,Y,Z(x,y,z)=PX(x)PZ∣X(z∣x)PY∣Z(y∣z). Then X and Y are independent given Z? True or False Suppose random variables X and Y are independent given Z , then the joint distribution must be of the form PX,Y,Z(x,y,z)=h(x,z)g(y,z), where h,g are some functions? True or false
X and Y are random variables (a) Show that E(X)=E(B(X|Y)). (b) If P((X x, Y ) P((X x})P({Y y)) then show that E(XY) = E(X)E(Y), i.e. if two random variables are independent, then show that they are uncorrelated. Is the reverse true? Prove or disprove (c) The moment generating function of a random variable Z is defined as ΨΖφ : Eez) Now if X and Y are independent random variables then show that Also, if ΨΧ(t)-(λ- (d) Show the conditional...
2. A random vector (X,Y) is uniformly distributed in a triangle with vertices ABC, having coordinates A(0,0), B(2.0), C(0,1). The joint density f(x,y) is given by the formula 141) - f(x,y) = { s 15 inside the triangle outside
Find an example of two dependent binomial random variables X and Y with same probability of success p that when you add them X+Y the result is not a binomial random variable.