An individual who has automobile insurance from a certain company is randomly selected. Let X be the number of moving violations for which the individual was cited during the last 3 years. The pmf of X is x 0 1 2 3 p(x) 0.5 0.3 0.15 0.05 Compute E(X) and V(X) Suppose an individual with X violations incurs a surcharge of $ (50 X^2 200 X). Calculate the expected amount of the surcharge.

The table below represents the displacement of a fish from its reef as a function of time: time (hours) x displacement from reef (feet) y 0 4 1 64 2 124 3 184 4 244 part a: what is the y-intercept of the function, and what does this tell you about the fish? (4 points) part b: calculate the average rate of change of the function represented by the table between x = 1 to x = 3 hours, and tell what the average rate represents. (4 points) part c: what would be the domain of the function if the fish continued to swim at this rate until it traveled 724 feet from the reef? (2 points)