Calculate the probability that X + Y < 3, where X and Y have joint prob- ability density (2xy +2x + y) 0 < x < 3, 0 < y < 3 p(x, y) = otherwise

Q: Find the density of Z = X-Y for independent Exp(λ) random varibles X and Y. Show all Work!!

A: X and Y are independent random variables each with  Exp(λ)

Q: Evaluate f(x, y, z) dV for the function f(x, y, z) = xz² and region B = [0, 3] × [5, 7] × [4, 5].

A:

Q: For a special fully continuous last survivor insurance of 1 on two independent lives, (x) and (y).…

A: two independent lives are given x and y are independent

Q: 9. If X, Y have some bivariate density, prove that Var(X – Y) = Var(X)+Var(Y) – 2Cov(X,Y).

A: We have given that X and Y are random variables having some bivariate density.

Q: A system consisting of one original unit plus a spare can function for a random amount of time X. If…

A: If a system consists of  original unit plus a spare, then it can function for a random amount of…

Q: Evaluate 2æz dV where E = {(x, y, 2) | 2 < * < 3, z < y < 2x, 0 < z< z + 2y}

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Q: Let X, denote the mean of a random sample of size n from a Gamma(, 1) distribution. Show that Vn (X,…

A:

Q: Find the aven bounded by y=x and y =x+2

A: First draw the graph of the function and find the intersection point of the graph:

Q: X and Y are continuous random variables with pdf f(x,y) = 2x for 0 ≤x ≤y ≤1, and f(x,y) = 0…

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Q: f(z) = ze-32*. Please determine the average value of f over the interval [1, 3].

A:

Q: Suppose the location of a particle in the plane is restricted to be within the region of the first…

A: The joint pdf of X and Y is, fx,y=αxyI0,1xI0,x2y         =αxy, 0&lt;x&lt;1, 0&lt;y&lt;x2

Q: Consider (X1, X2, X3) with the joint pdf f(x1, 12, 13) x exp{-} (x² + x² + x} - {₁x2-x2x3)}. The…

A: The joint pdf of :The full conditions for  and : and

Q: (b) Calculate dx ds ду ds dz ds II || ||

A:

Q: Let X ~ Uniform(-1,1) and Y = X² , find the CDF and PDF.

A: Use the following definitions, to obtain the solution. The cumulative distribution function of a…

Q: a) Show the this function as density possibility like proof b)find the median value

A:

Q: A random point is chosen inside the unit square {(x ,y ) : 0 <= x,y <= 1}. What is the expected…

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Q: Suppose initially (t = 0) that the traffic density p = p_0 + epsilon * sinx, where |epsilon| << p_o.…

A:

Q: Let i, j, k e Za and w, x, y e Zb with i, j, k all different from each other and w, x, y all…

A: Let the number of elements in the domain be equal to m, and the number of elements in Zb be equal to…