Based on long years of experience, an instructor in the principles of economics has determined that in her class the probability distribution of X, the number of students absent on Mondays, is as follows:

col1 X: 0 1 2 3 4 5 6 7
col2 F(x)0.005 0.025 0.310 0.340 0.220 0.080 0.019 0.001

(a) Sketch a probability function of X
(b) Find the probability that on a given Monday either two or three or four students will be absent
(c) Find the probability that on a given Monday more than three students are absent
(d) Compute the expected value of the random variable X. Interpret this expected value.
(e) Compute the variance and standard deviation of the random variable X
(f) Compute the expected value and variance of Y=7X+3