Question: Over the last 10 years, a company's annual earnings increased from the previous year seven times and decreased from the previous year three times. You decide to model the number of earnings increases over the next decade as a binomial random variable.

(a) What is your estimate of the probability of success p, defined as an increase in annual earnings?

For parts b, c, and d of this problem, take the estimated probability as the actual probability for the next decade (number of trials is ten).

(b) What is your estimate that earnings will increase in exactly 5 of the next years?

(c) Calculate the expected number (mean of the probability distribution) of yearly earnings increases over the next 10 years.

(d) Calculate the variance and standard deviation of the number of yearly earnings increases over the next 10 years.