As an experiment, we pick people at random and ask their birthdays. Assume for t
ID: 3133832 • Letter: A
Question
As an experiment, we pick people at random and ask their birthdays. Assume for this problem that there are 365 days in a year (so we will not consider February 29), and that each date is equally likely to be the person's birthday. Define a random variable X on the sample space (the sample space is all possible days in the year) by the formula X (date) = (number of birth month)/(number of birth date). So for example, since July is the 7th month of the year, we have X(July 4) = 7/4 = 1.75 and X (July 14) = 7/14 = 0.5. What is X(January 29)? What is A (June 6)? What is P(X - 15)? What is P(X is an integer)?Explanation / Answer
a)
As Jan 29 is 1/29,
X(Jan 29) = 1/29 = 0.034482759 [ANSWER]
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b)
As June 6 is 6/6,
X(June 6) = 6/6 = 1 [ANSWER]
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c)
This is impossible, as no month is greater than 15 and the date is always greater than 1 (dec 1 has the maximum X, X = 12).
Hence,
P(x = 15) = 0 [ANSWER]
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d)
There are 365 days.
For January, there is 1 integer.
For Feb, there are 2 integers.
For Mar, there are 2 integers.
For Apr, there are 3 integers.
For May, there are 2 integers.
For Jun, there are 4 integers.
For Jul, there are 2 integers.
For Aug, there are 4 integers.
For Sep, there are 3 integers.
For Oct, there are 4 integers.
For Nov, there are 2 integers.
For Dec, there are 6 integers.
Hence, a total of 35 integers.
Hence,
P(x is an integer) = 35/365 = 0.095890411 [ANSWER]
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