Due date: Thursday 2/5, 11:59pm
Bernoulli process
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Link to originalPMF and CDF: number of heads in five flips
Let
count the number of heads resulting from five flips of a coin. Write complete formulas (using cases) for the PMF and CDF of
.
Solution
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Link to originalIntersection accidents
Suppose that the odds of an accident occurring on any given day at the intersection of Ivy and Emmet is 0.05.
What are the odds of the first accident occurring between day 5 and day 10, inclusive? (Use an RV with an appropriate discrete distribution type.)
Solution
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Link to originalLottery game
Suppose a lottery game requires that you purchase a $10 game card and advertises a 10% probability of winning a prize.
If you keep purchasing these game cards until you win twice, what is the probability you will purchase at least 4 of them?
Be sure to define a random variable and name the type of distribution that it has.
Solution
Expectation and variance
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Link to originalVariance from CDF: Drill bit changes
The bits for a particular kind of drill must be changed fairly often. Let
denote the number of holes that can be drilled with one bit. The CDF of is given below: (a) Find the probability that a bit will be able to drill more than 2 holes.
(b) Find
by constructing the PMF.
Solution
Review problems
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Link to originalReliability - Math competition cutoff score
At a high school math competition, students take a test with 10 questions. Each question is worth one point and the probability of a student getting any one question correct is 0.55, independent of the other questions.
(a) Find the probability of a student getting a score of 8 or higher.
(b) Students take the test individually but compete in teams of 2. To proceed to the second round of competition, each student on the team must score at least 8. Each high school can enter 2 teams. If a high school enters two teams, find the probability at least one of their teams will make it to the second round. Assume students’ scores are independent.
Solution