# Statistics- A ﬁrm’s revenue distribution for the coming year

March 30, 2017

Question
1.Consider a 24-sided die, with sides numbered 1 to 24 (so that the sample space of outcomes is {1,2,…,24}). Suppose that all outcomes are equally likely. What is the mean and variance of the outcome of a roll of a 24-sided die?

2. A ﬁrm’s revenue distribution for the coming year is (in million dollars): 15% probability of 5, 25% probability of 10, 20% probability of 12, 30% probability of 14 and 10% probability of 20. If F(.) is the cumulative distribution function of this random variable, what is F(11) equal to? What is F(14)? What is the variance of the ﬁrm’s revenue distribution?

3. The world incidence of (frequency of world population having) diabetes is 5%. If 20 persons are chosen at random, what is the probability that no more than 3 have the disease?

4. Two jars contain coins. Jar I contains 7 pennies, 6 nickels and 8 dimes. Jar II contains 5 pennies, 3 nickels and 1 dime. A jar is selected at random and a coin is selected from that jar. If the coin is a nickel, what is the probability that it came from jar II?

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