Supposc X takes on values 0, 1, and 2 with equal probability and Y takes on value 3 with probabil...
The discrete random variables X and Y take integer values with joint probability distribution given by f (x,y) = a(y−x+1) 0 ≤ x ≤ y ≤ 2 or =0 otherwise, where a is a constant. 1 Tabulate the distribution and show that a = 0.1. 2 Find the marginal distributions of X and Y. 3 Calculate Cov(X,Y). 4 State, giving a reason, whether X and Y are independent. 5 Calculate E(Y|X = 1).
question 4, 3 sub-questions Final2.jpeg iat probability density function is given by f(x, y (2(x2+ y'), 0<x <2, 0cy3 Find the marginal densities of X and Y. Lip 2 Are X and Y independent? 4p c. Find probability X + Y < i , P(X+Y < 1 ). The amount of time, in hours, that a computer functions before breaking down .b] uniformly distributed on [o is continuous random variable T
3. Consider the joint probability distribution for Y and X. X/Y 2 4 6 1 0.2 0.21 2 10 201 3 5.2 0 2 a) Calculate the marginal densities for both Y and X. b) Show using the conditional distribution for Y and the marginal distribution for Y, that X and Y are not independent. c) Calculate the E(Y|x = 1)and V(Y | x = 1).
Consider the bivariate function f(x.y) = (x + y)/3 for 0< x< 1 and 0<y< 2 and f(x.y) = 0 3. otherwise. (a) Show that f(xy) is a density function. (b) Find the probability that both X and Y are less than one. (c) Find the marginal densities of X and Y and show that they are not independent. (d) Find the conditional density of X given Y when Y = 0.5.
1. The joint probability density function (pdf) of X and Y is given by fxy(x, y) = A (1 – xey, 0<x<1,0 < y < 0 (a) Find the constant A. (b) Find the marginal pdfs of X and Y. (c) Find E(X) and E(Y). (d) Find E(XY). 2. Let X denote the number of times (1, 2, or 3 times) a certain machine malfunctions on any given day. Let Y denote the number of times (1, 2, or 3...
Let X and Y be jointly continuous random variables with joint probability density given by f(x, y) = 12/5(2x − x2 − xy) for 0 < x < 1, 0 < y < 1 0 otherwise (a) Find the marginal densities for X and Y . (b) Find the conditional density for X given Y = y and the conditional density for Y given X = x. (c) Compute the probability P(1/2 < X < 1|Y =1/4). (d) Determine whether...
Let X and Y be jointly continuous random variables with joint probability density given by f(x, y) = 12/5(2x − x2 − xy) for 0 < x < 1, 0 < y < 1 0 otherwise (a) Find the marginal densities for X and Y . (b) Find the conditional density for X given Y = y and the conditional density for Y given X = x. (c) Compute the probability P(1/2 < X < 1|Y =1/4). (d) Determine whether...
6. (Entropy) The Bernoulli random variable X takes on the values 0, 1 with equal probability, i.e. PX pX Compute El(x) if where logs are to base 2
Please show the steps and the answers Suppose (X, Y) takes values on the unit square [0, 1] x [0, 1) with joint pdf f(x,y)- 3. (x2 + Y2). a) Find the marginal probability density function fx(x) and use it to find P(X < 0.5). b) Find the joint distribution function.
The joint density of random variables X and Y is given to be f(x,y) =xy^2 for 0≤x≤y≤1 and is 0 elsewhere. (a) Compute the marginal densities for X and for Y respectively. (b) Compute the expected valueE(XY). (c) Define a new random variable W=Y/X. Compute the probability P(W > t) for anyt >1. Also find the probability P(W <1/2) ?