Let x and y be independent exponential random variables with pa- rameter u > 0 and let z = x +y. (a) compute the density of z by using the convolution formula rtoo fz(z) = | fx (x) • fy(z – x) dx. -00 be precise on the domain for z and on the integration bounds for x in the above integral. (b) find the joint cumulative distribution function f(x, z)(x, z) of the random variables x and z. (c) find the joint density function f(x, z)(x, z) of x and z. hint: recall that əroz f(x, z)(x, z) = f(x, z)(x, z). (d) compute e[x|z = z]. 22

The average hourly earnings for a construction worker is projected to be $24.50 in 2012. jason wants to join the construction work force after he graduates in 2012. his friend tells him that average hourly earnings for construction workers will rise by 2% from 2009 to 2012. based on the data below, assuming that the projected hourly earnings are correct, is jason’s friend’s statement accurate? construction industry - average hourly earnings, 2000-2009 a. his friend’s statement is accurate. the average hourly earnings will increase by 2%. b. his friend’s statement is not accurate. the percent increase will be more than 2% c. his friend’s statement is not accurate. the percent increase will be less than 2% d. his friend’s statement is not accurate. the average hourly earnings will decrease

Jahdzia wears her winter coat when the temperature is colder than -4 degrees celsius. write an inequality that is true only for temperatures (t) at which jahdzia wears her winter coat.

Type the next three numbers in a sequence 80, 90, 85, 95, 90, 100, 95, 105