3. A random variable Z, which is the number of Computer Labs in EconS 311 skipped during the semester, has the following distribution: Z f(Z) 0 5k 1 2k 2 2k 3 k

(a) What does the constant k have to be equal to for this to be a distribution function? Why? (b) Find the Prob(Z=0); Prob(Z=3); and Prob(0 < Z <3). (c)

Calculate the expected value of Z. (d) Calculate the variance and standard deviation of Z?