Probability, percentile, PDF, and PMF. Use the companion software PARSE to

(a) Plot the PDF curve of the chi-square distribution with = 2.7 and 5 degrees of free- dom.

(b) Plot the PMF curve of the binomial distribution with N = 30 and p = 0.32.

(c) Calculate the probabilities P {X 4.4} and P {2.5 < X 5.7}, where X is a RV

having the log-normal distribution with = 1.2 and = 2.9.

(d) Calculate the 37% and 89% percentile points of the chi-square distribution with =

3.4 and 6 degrees of freedom.

(e) CalculatetheprobabilityP{X m}ofaPoissonRVX for = 2.4andm = 0,2,50,

respectively. Compare the results with your theoretical calculation for m = 0, 2.