5) X and Y are jointly continuous with joint pdf ( , ) = ≤ , ≤
a- Verify that the f(x, y) is a joint probability density function
b- Find the marginal mass function of x
c- Find the marginal mass function of y
d- Are X and y independent (Why)
e- Find E(X) and find E(Y)
f- conditional expectation of Y given X = x

What is (28 + 7 + 6 + 3) x 1/2 show your work

An automated water dispenser fills packets with one liter of water on average, with a standard deviation of 5 milliliter. the manual says that after a year of operation the dispenser should be tested to see if it needs recalibration. a year later a number of filled packets are set aside and measured separately. it is found that the average packet now contains about 0.995 liters. does the dispenser need calibration? explain your answer.

Which expression is equivalent to 8(k + m) − 15(2k + 5m)?