A random number between 1 and 12 is generated to decide on the hour during wh...

A random number between 1 and 12 is generated to decide on the hour during which a
special contest will be played on a radio station.

a) Explain why this must be a uniform distribution

b) Develop the probability distribution for the contest hour

c) Calculate the expected outcome.
Expert Answer

a) This is a uniform distribution since all the outcomes from 1 to 12 are equally likely in this case. Hence , this is a uniform distribution

b) Probability distribution will be 1/12 for all the numbers between 1 to 12

c) Expected Outcome = 1/12 * (1 + 2 + 3 + 4 + 5 + 6 + 7 + 8 + 9 + 10 + 11 + 12) = 6.5

Hence the expected outcome will be equal to 6.5