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Probability - IIntroduction to Probability - Exam, Exams of Probability and Statistics

Alliance UniversityProbability and Statistics

This is the Exam of Introduction to Probability which includes White and Blue, Probability, Ties, Three Colours, Probability, Fifth Card, Queen, Smith Travels, Cumulative Distribution, Function etc. Key important points are: Probability, One Denomination, Fifth Card, Queen, Smith Travels, Vancouver, Berlin, Frankfurt and Calgary, Luggage, Probability

Typology: Exams

2012/2013

Uploaded on 02/21/2013

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April 2005 MATH 302 Section 201 Name: 1
1) A poker hand consist of 5 cards out of a deck of 52.
a) What is the probability of a Full House, that is, three cards of one denomination
and two cards of a second denomination. [5]
b) What is the probability of One Pair, that is, two cards from one denomination,
with the third, fourth and fifth card from a second, third, and fourth denomina-
tion, respectively: for example two 8’s, a king, a queen and a 4. [5]
pf3
pf4
pf5
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pf9

Partial preview of the text

Download Probability - IIntroduction to Probability - Exam and more Exams Probability and Statistics in PDF only on Docsity!

  1. A poker hand consist of 5 cards out of a deck of 52.

a) What is the probability of a Full House, that is, three cards of one denomination and two cards of a second denomination. [5]

b) What is the probability of One Pair, that is, two cards from one denomination, with the third, fourth and fifth card from a second, third, and fourth denomina- tion, respectively: for example two 8’s, a king, a queen and a 4. [5]

  1. Mrs Smith travels from Berlin to Vancouver via Frankfurt and Calgary. There is a 5% chance that her luggage is left behind in Berlin. If it is not left behind in Berlin, there is a 7% chance that it is left behind in Frankfurt. If it not left behind in Berlin or Frankfurt, there is a 10% chance that it is left behind in Calgary.

a) What is the probability that she can claim her luggage in Vancouver? [5]

b) Suppose that her luggage was left behind. What is the probability that it was left behind in Calgary? [5]

  1. On average, two cars in a hundred brake due a particular mechanical failure (in- dependently of each other) which can only be detected in a complex check. Use the Poisson approximation to the Binomial distribution to estimate how many cars should be tested in order that the probability is at least 0.95 that at least one of the cars will have the defect. [10]
  1. Let X and Y be continuous random variables with joint density function

f (x, y) =

e−y^ if 0 ≤ x ≤ y < ∞ 0 elsewhere

a) Find P(Y ≥ 2 X) and P(Y ≤ 2 X). [10]

b) Determine the covariance of X and Y. [10]

  1. An exam has 100 true/false questions. Suppose a student knows the correct answers to 36 questions, but chooses true/false with equal probability for the remaining ques- tions. Use the normal approximation to the binomial to estimate the probability that the students gets 72 questions or more correct. [10]
  1. Mr Smith invests $100.000 equally in four uncorrelated assets whose annual returns r 1 ,... , r 4 are normally distributed with respective means 8%, 10%, 12%, and 14% and standard deviations 6%, 7%, 5%, and 12%, respectively. What is the probability that, after one year, Mr Smith’s net profit from this investment is at least $15.000? [10]