Assume a discrete distribution for the number of possible sunny days in Provo, Utah during the week of April 20 through April 26. For this discrete distribution, p(x) = 0 when x cannot occur, or p(x) > 0 if it can. Based on this information, what is the probability of it being sunny on 5 days and on 10 days during the week, respectively?
A. A positive value; zero.
B. A positive value; infinite.
C. Zero; infinite.
You can answer this question without any information whatsoever about the probability distribution; answers B and C are wrong for any probability distribution.
0 ⤠P(E) â¤1: the probability of any event E is a number between 0 and 1. The probability of 0 means that the event can never happen and the probability of 1 means that the event is certain to happen.
The sum of the probabilities of any list of mutually exclusive and exhaustive events equals 1.
Billâs method is the fastest, but if you want to see that A is indeed correct:
The first part asks for the probability that are days of sun from April 20 to April 26. Thatâs a time period of 7 days. Clearly 7 days > 5 days, which means itâs possible that there could be 5 sunny days.
You are also given that p(x) = 0 when x cannot occur, or p(x) > 0 if it can.
Since this outcome is possible, it must have positive probability.
For the second part, you are asked the same thing, but instead of 5 days, you are given 10 days.
Clearly, 10 days canât fit in a time period of 7 days, so the outcome is not possible.
You are given that p(x) = 0 when x cannot occur, or p(x) > 0 if it can.
Since the outcome canât happen, the probability is zero.