18:34 0.0KB/s ← Review Exercises ST2501 Review Exercises September 3, 2024 4G 244 © 1. An urn contains 4 balls numbered 1, 2, 3, 4, respectively. Let Y be the number that occurs if one ball is drawn at random from the urn. What is the probability function for Y? 2. Consider the urn in Exercise 1. Two balls are drawn from the urn without replacement. Let W be the sum of the two numbers that occur. Find the probability function for W. Compute μw and σw 3. Assume the sampling in Exercise 2 is done with replacement and define random variable W in the same way. Find the probability function for W and compute its mean and standard deviation. 4. An urn contains five balls numbered 1 to 5. Two balls are drawn simultaneously. a) Let X be the larger of the two numbers drawn. Find the proba- bility mass function for random variable X. b) Let V be the sum of the two numbers drawn. Find the probability mass function for random variable V. c) For the random variables in a) and b), find μx, σx, μy and σy. 5. A class in statistics contains 10 students, 3 of whom are 19, 4 are 20, 1 is 21, 1 is 24, and 1 is 26. Let X be the average age of the 2 randomly selected students and derive the probability function for X. 6. A man has four keys in his pocket and, since it is dark, cannot see which is his door key. He will try each key in turn until he finds the right one. Let X be the number of keys tried (including the right one) to open the door. What is the probability function for X? 日 1 色」 Page View mode Edit Share 1
18:34 0.0KB/s ← Review Exercises ST2501 Review Exercises September 3, 2024 4G 244 © 1. An urn contains 4 balls numbered 1, 2, 3, 4, respectively. Let Y be the number that occurs if one ball is drawn at random from the urn. What is the probability function for Y? 2. Consider the urn in Exercise 1. Two balls are drawn from the urn without replacement. Let W be the sum of the two numbers that occur. Find the probability function for W. Compute μw and σw 3. Assume the sampling in Exercise 2 is done with replacement and define random variable W in the same way. Find the probability function for W and compute its mean and standard deviation. 4. An urn contains five balls numbered 1 to 5. Two balls are drawn simultaneously. a) Let X be the larger of the two numbers drawn. Find the proba- bility mass function for random variable X. b) Let V be the sum of the two numbers drawn. Find the probability mass function for random variable V. c) For the random variables in a) and b), find μx, σx, μy and σy. 5. A class in statistics contains 10 students, 3 of whom are 19, 4 are 20, 1 is 21, 1 is 24, and 1 is 26. Let X be the average age of the 2 randomly selected students and derive the probability function for X. 6. A man has four keys in his pocket and, since it is dark, cannot see which is his door key. He will try each key in turn until he finds the right one. Let X be the number of keys tried (including the right one) to open the door. What is the probability function for X? 日 1 色」 Page View mode Edit Share 1
Chapter8: Sequences, Series,and Probability
Section8.7: Probability
Problem 38E
Related questions
Question
Transcribed Image Text:18:34 0.0KB/s
← Review Exercises
ST2501 Review Exercises
September 3, 2024
4G
244
©
1. An urn contains 4 balls numbered 1, 2, 3, 4, respectively. Let Y be
the number that occurs if one ball is drawn at random from the urn.
What is the probability function for Y?
2. Consider the urn in Exercise 1. Two balls are drawn from the urn
without replacement. Let W be the sum of the two numbers that
occur. Find the probability function for W. Compute μw and σw
3. Assume the sampling in Exercise 2 is done with replacement and define
random variable W in the same way. Find the probability function for
W and compute its mean and standard deviation.
4. An urn contains five balls numbered 1 to 5. Two balls are drawn
simultaneously.
a) Let X be the larger of the two numbers drawn. Find the proba-
bility mass function for random variable X.
b) Let V be the sum of the two numbers drawn. Find the probability
mass function for random variable V.
c) For the random variables in a) and b), find μx, σx, μy and σy.
5. A class in statistics contains 10 students, 3 of whom are 19, 4 are 20, 1
is 21, 1 is 24, and 1 is 26. Let X be the average age of the 2 randomly
selected students and derive the probability function for X.
6. A man has four keys in his pocket and, since it is dark, cannot see
which is his door key. He will try each key in turn until he finds the
right one. Let X be the number of keys tried (including the right one)
to open the door. What is the probability function for X?
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