Think of the Situation of Rolling Two Dice and Let

question 28

Essay

Think of the situation of rolling two dice and let M denote the sum of the number of dots on the two dice. (So M is a number between 1 and 12.)
(a)In a table, list all of the possible outcomes for the random variable M together with its probability distribution and cumulative probability distribution. Sketch both distributions.
(b)Calculate the expected value and the standard deviation for M.
(c)Looking at the sketch of the probability distribution, you notice that it resembles a normal distribution. Should you be able to use the standard normal distribution to calculate probabilities of events? Why or why not?

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Definitions:

Maximizing

The strategy of seeking the best possible outcome or the highest possible utility when making a decision.

Availability Heuristic

A cognitive bias that causes people to overestimate the probability of events associated with memorable or vivid examples.

Satisficing

A decision-making strategy that entails selecting the first option that meets a minimum set of criteria, rather than optimizing.

Heuristic

Cognitive shortcuts or rules of thumb that simplify decision making, often at the expense of accuracy or completeness.