3. Given the consumption function C = 0 -by (with a > 0:0 <b< 1): (0)...
2.5.1. The probability function of a random variable Y is given by where λ is a known positive value and c is a constant. (a) Find c. (b) Find P(Y 0). (c) Find P(Y>2).
Suppose that X is a continuous random variable whose probability density function is given by (C(4x sa f(x) - 0 otherwise a) What is the value of C? b) Find PX> 1)
The production function for a commodity is given by Q=43x4 y , with -1<a<0 and -1<B<0 as assumptions. O is output, x is the first factor input, and y is the second factor input. Find the marginal product associated with each factor input (assuming the other factor input does not change). Is marginal product increasing or decreasing with increased usage of the factor in question?
10. Consider this joint pdf. c(r+ y 0 otherwise (a) Find c. (b) Find frv). (c) Find fyy) (d) What is the probability that x > 0 giveny-1?
4. (20 points) Consider the demand function D(p;m) mP, where > 0 is consumers' average income. The supply consists of a monopoly, whose revenue from sales is given by R(p;mpD(p;m) (a) (5 points) Compute the elasticity function, E(p;m)-D'(p;m) b) (5 points) Find the value of p such that E(p; (c) (5 points) Compute the marginal revenue function, MR(p; m) R'(p; (d) (5 points) What is the solution to the equation MR (p 0? Compare 1 your answer to your answer...
Let X and Y have joint probability density function fx,y(x,y) = e-(z+y) for 0 x and 0 y. Find (a) Pr(X=y (b) Prmin(X, Y) > 1/2) (c) Pr(X Y) d) the marginal probability density function of Y (e) E[XY].
7. The random variables X and Y have joint probability density function f given by 1 for x > 0, |y| 0 otherwise. 1-x, Below you find a diagram highlighting the (r, y) pairs for which the pdf is 1 (a) Calculate the marginal probability density function fx of X (b) Calculate the marginal cumulative distribution function Fy of Y (c) Are X and Y independent? Explain.
7. The random variables X and Y have joint probability density function f given by 1 for x > 0, |y| 0 otherwise. 1-x, Below you find a diagram highlighting the (r, y) pairs for which the pdf is 1 (a) Calculate the marginal probability density function fx of X (b) Calculate the marginal cumulative distribution function Fy of Y (c) Are X and Y independent? Explain.
1. The probability mass function of a random variable X is given by Px(n) bv P Yn (a) Find c (Hint: use the relationship that Σο=0 (b) Now assume λ = 2, find P(X = 0) (c) Find P(X>3) n-0 n! ex)
Which position reacts most rapidly under Friedel-Crafts alkylation conditions (B)-> OCH3 (D) (C) (A)