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?
What will be an ideal response?
Answer:
(a)
(b) 7.0; 2.42.
(c) You cannot use the normal distribution (without continuity correction) to calculate probabilities of events, since the probability of any event equals zero.
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