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Quiz 1. CS567 Spring 2006
10 minutes. 10 points.
Write your name BEHIND this sheet of paper and give brief answers to the following
questions.
1) What range of values can a probability mass function take? What range of values
can a probability density function take? What range of values can a cumulative
distribution function take?
2) Given the joint distribution of 2 random variables X & Y, how would you
calculate the marginal distribution of X?
3) In each of these pairs, which is the data and which is the model:
a. Photograph and Person
b. Scatter Plot, Line fit
4) How would you calculate the probability of getting an A in this course?
5) What is the probability that 2 students in this class share the same birthday (ignore
year and assume there is not such thing as a leap year)?
Total permutations of birthdates = 365n
How many pairs of students could share a particular birthdate? nC2
How many birthdates could be shared? 365
How many ways to share a particular birthdate? 365 * nC2
Quiz 1. CS567 Spring 2006
10 minutes. 10 points.
For every shared birthday, how many permutations of birthdays could the remaining
students have? 364Pn-2
Ans: 364Pn-2 *3 65 * nC2/365n
But above is for exactly 2 sharing a birthday. What about the probability of at least 2
sharing any birthday? First calculate probability of this not happening.
Coin version: Probability of not repeating a side is zero for n > 2. For n = 2, probability =
½. Hence probability of some kind of match = ½.
For die: For n < 7, probability of not repeating a number is 6Pn/6n
Birthday version: For n < 366, probability of not repeating a birthday is 365Pn/365n
Hence probability of repeating some birthday at least once = 1 – 365Pn/365n
Quiz 1. CS567 Spring 2006
10 minutes. 10 points.
NAME: