f(x, y) = x+y where 0.2 < x < 0.5 and 5.0 < y < 10.0 and zero otherwise
What is the p(x+y > 10)?
Given f(x,y) = [x*sqrt(y)] / 3224 , 0<x<y<5.76 (f(x,y)= 0 otherwise) Find P(x + y > 0.5 | x = 1/5)
Suppose that a random variable X has the following pdf: 8px+2(1-P) 0<x<0.5., JxX;P) = *; where 0 Sp Si 0 otherwise where p is simply a constant that has yet to be specified in other words, p is a parameter). For now, we will leave the parameter p an unspecified constant ► Find P(X>0.3) = Note: your answer will be an expression containing p. Suppose that k> 0 is also a constant (not yet specified). Find the expected value of...
Q5. Suppose the joint pdf of X, Y is given by f(x, y) zy/3 if 0 s S1 and 0 sy< 2 and f(x,y) elsewhere. a. Compute P(X+Y2 1). b. What is the probability that (X, Y) E A where A is the region bounded above by the parabola y 2 c. What is the probability that both X, Y exceeding 0.5? d. What is the probability X will take on values that are at least 0.2 units less than...
X and Y are random variables with the joint PDF: f(x,y)= cxy^2 where 0<=x<=9; 0<=y<=9 0 otherwise find: - constant c - P[min(X,Y) <= 4.5] - P[max(X,Y) <= 6.75]
The density f(x,y) is given by the formula f(x,y) = 8x(x + y), x ≥ 0, y ≥ 0, x + y ≤ 1 and zero otherwise. (a) Find the marginal distributions. (b) Find the conditional distribution of Y given X = x. (c) Find P(X ≤ 1/2, Y ≤ 1/2) (d) Find P(X ≤ 1/2) (e) Find P(Y ≤ 1/2 | X ≤ 1/2) (f) Find P(Y ≤ 1/2 | X = 1/2)
1. Two independent random variables X and y are given with their distribution laws 4 P 07 0.1 0.2 P 0.2 0.3 0.5 Find 1) the variance of random variable Y 2) the distribution law of random variable Z-0.5Y+x END TEST IN PROBABL ITY THEORY AND STAISTICS Variant 1 1. Two independent random vanables X and Y are given with their distribution laws: 2 0.7 0.1 P 0.2 0.3 0.5 0.2 Find 1) the variance of random varñable Y 2)...
Suppose a consumer had a utility function given by: U=X^0.5*Y^0.2. If the price of Good X (Px) is $10 and the price of Good Y is $2 then what is the utility maximizing quantity of Good Y the consumer will purchase with a budget of $98 (Round to the nearest two decimal places if necessary.)
The Cobb-Douglas production function for a product is N(x,y) = 10(x^0.8)(y^0.2) where x is the number of units of labor and y is the number of units of capital required to produce N units of the product. What is the marginal productivity of labor and the marginal productivity of capital? What are they when there are 40 units of labor and 50 units of capital? Nx(x,y) = Nx(40, 50) = Ny(x,y) = Ny(40, 50) = If each unit of labor...
1. Consider the following function: 4x 0<x<0.5 f(x)= 4- kx 0.5 <x<1 0 Otherwise a) (5%) Determine k such that f(x) is a probability density function. b) (6%) Determine CDF of x. c) (4%) Using CDE, what is the p(x 0.75) d) (4%) Using CDE what is p(x<0.6) e) (4%) Determine E(x) Type here to search o TT
Let random variable X be distributed according to the p.m.f P(a) 0.3 0.5 0.2 · If Y = 2x, what are ELY Var(Y) If Z = aX + b has E121 = 0 and Var(Z) = 1, what are: .