Expected value for binomial distribution:
1. Let X denote the prison sentence, in years, for people convicted of auto theft in a particular state in the United States. Suppose that the pdf of X is given by(Requires Calculus)
f(x) = (1/9)x2, 0 < x < 3
Use integration to find the expected prison sentence.
2. If the basket ball player is a 74% free throw shooter, then, on average, how many free throws will he or she make in a game with eight free throw attempts?
3. Let X denotes the annual salary of university professors in the United States, measured in thousands of dollars. Suppose that the average salary is 52.3, with a standard deviation of 14.6. Find the mean and standard deviation when salary is measured in dollars.