uppose that cars arrive at a traffic light according to a Poisson process with a rate of one car per minute starting from time t = 0 minutes. Determine a. The probability that no cars arrive in the rst two minutes. b. The probability that no cars arrive ever. c. The probabilit...
A person repeatedly and independent flips a fair coin to decide whether to take a step to the left or to the right from a point X. Determine the expected number of times the person returns to X.
A floor consists of parallel planks which have a two foot width. A circular disc of diameter one foot is randomly and uniformly dropped onto the planks. Determine the probability that the disc does not touch the line between two planks. Determine also the expected distance fro...
You want to know which month had the highest percentage of rainy days for your city last year. Your investigation gave the following results: March had 5 days of rain, April had 8 days of rain, May had 3 days of rain. For each month, what percentage of the month had rainy days...
Chris wants to make an enclosed rectangular area for a mulch pile. She wants to make the enclosure in such a way as to use a corner of her back yard. She also wants it to be twice as long as it is wide. Since the yard is already fenced, she simply needs to construct two sides ...
Charles wants to build a vegetable garden such that three sides of the garden are fenced and the fourth side of the garden will be the existing back fence. He has 30 feet of fencing available. Find the dimensions of the garden that will produce the maximum enclosed area
Henry has $240 more than my cousin Joe, who has $150 more than my friend Ann. Together the three people have $990. The amount Ann has, in dollars, is: a. $150 b. $200 c. $390 d. 450 e. $600