Math 501. 4th Homework. Due Wednesday, October 31, 2007. Homework on "Basic properties of Random variables and Expectation". Summary: Math 501. 4­th Homework. Due Wednesday, October 31, 2007. Homework on "Basic properties of Random variables and Expectation". 1. A real estate agent is selling a house. If the house is sold within the first month after the home hits the market, the real estate agent makes \$3000. If the house is sold within the second month, the real estate agent makes \$2000. If the house is sold within the third month, the real estate agent breaks even. If the house is not sold by three months, the real estate agent losses \$4000. The probability that the house is sold within the i­th month is 1 2i , for i = 1, 2, . . . . What is the real estate agent expected profit? 2. Find two r.v.'s X1 and X2 such that: (i) For each a < b, P[a < X1 b, a < X2 b] = P[a < X1 b]P[a < X2 b]. (ii) X1 and X2 are not independent r.v.'s. 3. Find two r.v.'s X1 and X2 such that: (i) Both X1 and X2 have a continuous distribution. (ii) X1 + X2 does not have a continuous distribution. 4. The random variables X and Y have joint density function f(x, y) = 3x if 0 x y 2x 2, 0 otherwise. (i) Find P[Y 1]. Collections: Mathematics