Posted by Mon Feb 26. Due: MON Mar 4.
Note: this hw set is “half” of a set, because it is due Monday before
midterm. It serves to wrap up discrete distributions so you are ready
for the midterm exam!
(Do you see how this is a “waiting” random variable in both problems 1
and 2?)
Homework set 9 will be longer by approximately same amount this one is shorter than the average. :)
Solve exercise 5.50:
Find the probability that a person flipping a coin gets
Solve exercise 5.51:
Three people toss a fair coin and the odd one pays for coffee. If the coins all turn up the same, they are tossed again. Find the probability that fewer than 4 tosses are needed.
Solve exercise 5.101 in the textbook.
The manufacturer of a tricycle for children has received complaints about defective brakes in the product. According to the design of the product and considerable preliminary testing, it had been determined that the probability of the kind of defect in the complaint was 1 in 10,000 (i.e., 0.0001).
After a thorough investigation of the complaints, it was determined that during a certain period of time, 200 products were randomly chosen from production and 5 had defective brakes.
Comment on the “1 in 10,000” claim by the manufacturer. Use a probabilistic argument. Use the binomial distribution for your calculations.
Repeat part (a) using the Poisson approximation.
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