Create, explore, and explain three unique, original examples of the application of the concept of expected value to some real-world situations.

For this assignment, I want you to apply the concept of "expected value" (The mean of a probability distribution of a random variable) in three specified, realistic areas.

1. 1)A lottery game (such as the NJ Pick 4, or MegaMillions, etc., NOT a scratch-off card )
2. 2)A casino game, as played in US casinos

3)A purchase of life-insurance by an individuals.

For each situation:

A) BRIEFLY describe it in terms of its statistical concepts and uncertainties (including, but not limited to, and explanation of : costs, how to win and how to lose, procedures, payouts, and profits, etc.).

B) Clearly define and state the random variable, and create a probability distribution. C) Calculate the expected value, showing your work or explaining your steps.

D) Finally, discuss the meaning or importance of the expected value, using full sentences and clear language that is not overly technicals.

Tips for creating the Probability Distribution, and for calculating the expected value :

For the lottery, use precision in describing how many numbers must be selected, and the size of the population from which to choose the selections.

For the casino game, you need not describe the entire game, and you can limit your analysis to one facet of the chosen game (for example, in roulette, you could address the probabilities involved in betting 'Odd' or 'Even', or betting a specific number, such as '22')

1. For the life insurance, please provide the actual premium and coverage amount for a friend, relative, or yourself. Find (on the internet) the statistical "probability of death in the next year" for that individual. Maintain confidentiality whenever you can.