ผลต่างระหว่างรุ่นของ "Probstat/homework 1"
Jittat (คุย | มีส่วนร่วม) |
Jittat (คุย | มีส่วนร่วม) |
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| แถว 9: | แถว 9: | ||
1. We are tossing N different balls into N bins. Each ball is equally likely to land in any bins. What's the probability that there is no empty bins? (I.e., empty bins are those with no balls landed on.) | 1. We are tossing N different balls into N bins. Each ball is equally likely to land in any bins. What's the probability that there is no empty bins? (I.e., empty bins are those with no balls landed on.) | ||
| − | 2. A biased coin tuns up head with probability 0.7. The probability that a random coin is biased is 0.1. Let event '''A<sub>k</sub>''' be the event that you toss the coin '''k''' times and the coin turns up all heads. Let event '''B''' be the event that the coin is biased. Compute the following conditional probability: '''P(B)''', '''P(B|A<sub>1</sub>)''', '''P(B|A<sub>2</sub>)''', '''P(B|A<sub>3</sub>)''', '''P(B|A<sub>4</sub>)''', and '''P(B|A<sub>5</sub>)'''. | + | 2. A biased coin tuns up head with probability 0.7. The probability that a random coin is biased is 0.1. Let event '''A<sub>k</sub>''' be the event that you toss the coin '''k''' times and the coin turns up all heads. Let event '''B''' be the event that the coin is biased. Compute the following conditional probability: '''P(B)''', '''P(B|A<sub>1</sub>)''', '''P(B|A<sub>2</sub>)''', '''P(B|A<sub>3</sub>)''', '''P(B|A<sub>4</sub>)''', and '''P(B|A<sub>5</sub>)'''. Plot the probabilities in a chart where the x-axis shows '''P(B|A<sub>i</sub>)''', where '''i''' ranges from 0 to 5. |
รุ่นแก้ไขเมื่อ 18:06, 3 กันยายน 2557
In these problems, please hand in your paper solutions. Don't just state the answers, but also show your work.
Basic problems
1. Work on problems 1, 3, 5, 7, 9, and 10 in Counting section in week2 practice 1.
2. (From FCP, Ch 2, Problem 13.) We have two bags. Bag A contains 4 red and 3 black balls. Bag B contains 4 red and 6 black balls. If a ball is randomly selected from each urn, what is the probability that the balls will be of the same color?
Challenging problems
1. We are tossing N different balls into N bins. Each ball is equally likely to land in any bins. What's the probability that there is no empty bins? (I.e., empty bins are those with no balls landed on.)
2. A biased coin tuns up head with probability 0.7. The probability that a random coin is biased is 0.1. Let event Ak be the event that you toss the coin k times and the coin turns up all heads. Let event B be the event that the coin is biased. Compute the following conditional probability: P(B), P(B|A1), P(B|A2), P(B|A3), P(B|A4), and P(B|A5). Plot the probabilities in a chart where the x-axis shows P(B|Ai), where i ranges from 0 to 5.
