Plot the cumulative probability distribution and probability distribution of the deal [0.1, 0; 0.2, 100; 0.6, 500; 0.1, 1000]. Determine the first moment graphically. Calculate the first four moments,...

Plot the cumulative probability distribution and probability distribution of the deal [0.1, 0; 0.2, 100; 0.6, 500; 0.1, 1000]. Determine the first moment graphically.

Calculate the first four moments, central moments, and cumulants of the following deals:

I. 0.5 probability of paying $100 and a 0.5 probability of paying zero; i.e. [0.5, 100; 0.5, 0].

II. The deal [0.1, 0; 0.2, 100; 0.6, 500; 0.1, 1000].