Consider the three graphs provided below.(a) One graph represents a probability density function (pdf), another represents its corresponding cumulative dis-tribution function (edf), and the third is neither. Determine which graph is which.(b) For each of the three graphs in part (a) explain how you knew which graphs were which. Your ansuer must usecomplete sentences and include a specific reason for each graph.Find the mean of this distribution described by the pdf,p(x)={-33500(x3-8x2-20x),00100otherwiseThe graph of a probability density function p(x)is given below. You should assume that p(x)=0 for all other valuesofx. Find the median of the distribution. Make sure to erplain how you got your ansuer in complete sentences.The following integral is a harder question. Evaluate extan(ex)dxtan(x).p(x)=0.5e-0.5x. What percentage of Alec's speechesare between 2 and 5 minutes long? Round your percentage to three decimal places if necessary. Hint: Don't rounduntil after you convert your decimal to a percentageThe Loyola University Chicago Math Department will hold a competition to see who can give the longest lectur