Annie and Alvie have agreed to meet between 5:00 p.m. and 6:00 p.m. for dinnerat a local health-food restaurant. Let X=Annie's arrival time and Y=Alvie's arrival time.Suppose X and Y are independent with each uniformly distributed on the interval [5, 6].a. What is the joint pdf of X and Y?b. What it the probability that they both arrive between 5:00 and 5:30 p.m.?

Given that: X= Annie's arrival time Y= Alvie's arrival time X and Y are uniformly distributed on the…

Answered: Annie and Alvie have agreed to meet…

Algebra and Trigonometry (MindTap Course List)

4th Edition

ISBN:9781305071742

Author:James Stewart, Lothar Redlin, Saleem Watson

Publisher:James Stewart, Lothar Redlin, Saleem Watson

Chapter14: Counting And Probability

Section14.2: Probability

Problem 3E: The conditional probability of E given that F occurs is P(EF)=___________. So in rolling a die the...

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The conditional probability of E given that F occurs is P(EF)=___________. So in rolling a die the conditional probability of the event E, getting a six, given that the event F, getting an even number, has occurred is P(EF)=___________.
Annie and Alvie have agreed to meet between 5:00 p.m.and 6:00 p.m. for dinner at a local health-food restaurant.Let X 5 Annie’s arrival time and Y 5 Alvie’s arrivaltime. Suppose X and Y are independent with each uniformlydistributed on the interval [5, 6].a. What is the joint pdf of X and Y?b. What is the probability that they both arrive between5:15 and 5:45?c. If the first one to arrive will wait only 10 min beforeleaving to eat elsewhere, what is the probability thatthey have dinner at the health-food restaurant? [Hint:The event of interest is A5{(x, y): u x2y u # 1y6}.]
A train’s arrival time at the station is T minutes past noon, where the PDF of T is given below. Given that the train hasn’t arrived by 12:05, what is the probability that it arrives by 12:10?
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A harried passenger will be several minutes late for a scheduled 10 A.M. flight to NYC. Nevertheless, he might still make the flight, since boarding is always allowed until 10:10 A.M., and boarding is sometimes permitted up to 10:30 AM. Assuming the end time of the boarding interval is uniformly distributed over the above limits, find the probability that the passenger will make his flight, assuming he arrives at the boarding gate at 10:25.
Suppose that the probability density function of a random variable X is as follows: f(x)= cx, for0<x<4; 0, otherwise. (a) Find c.(b) Find the cumulative distribution function F and sketch it.
The time for the first widget to be manufactured each morning is random between 1 and 3 seconds with a pdf of f(x)=1/162(x-3)^2(x+6) for 0 < x < 6What is the cumulative distribution function, F(x)? What is the probability of a widget being made earlier than 4 s?Answer to four decimal places What is the probability of a widget being made later than 1.3 s?Answer to four decimal places
Find (a) the mean of the distribution, (b) the standard devia- tion of the distribution, and (c) the probability that the random variable is between the mean and 1 standard deviation above the mean.The length (in centimeters) of the leaf of a certain plant is a continuous random variable with probability density function defined by ƒ(x) = 5/7 for x in [3, 4.4]
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