Question

Bob and Alice plan to meet between noon and 1 pm for lunch at the cafeteria....

Bob and Alice plan to meet between noon and 1 pm for lunch at the cafeteria. Bob’s arrival time, denoted by X, measured in minutes after 12 noon, is a uniform random variable between 0 and 60 minutes. The same for Alice’s arrival time, denoted byY.Bob’s and Alice’s arrival times are independent. We are interested in the waiting time W=|X−Y|.

i. What is the probability that W≤10 if X= 15?

ii. What is the probability that W≤10 if X= 5?

iii. What is average waiting time if X=x, where 0≤x≤60?

iv. What is the average waiting time?

Math   Statistics-And-Probability   
0 0
Add a commentTranscribed image text
Next >

Homework Answers

Answer #1

Let me know in the comment section if anything is not clear. I will reply ASAP!
If you liked the answer, please give a thumbs-up. This will be quite encouraging for me.Thank-you!

0 0
Know the answer?
Your Answer:

Post as a guest

Your Name:

What's your source?

Earn Coins

Coins can be redeemed for fabulous gifts.

Log In

Sign Up

Not the answer you're looking for?
Ask your own homework help question
Similar Questions
Alice, Bob, and Charlie each pick random numbers from the set {1, 2, 3, 4, 5,...
Alice, Bob, and Charlie each pick random numbers from the set {1, 2, 3, 4, 5, 6, 7, 8, 9, 10} independently. (a) What is the probability that Alice and Bob pick the same number? (b) What is the probability that Alice, Bob, and Charlie all pick even numbers? (c) What is the probability Alice’s pick is at most 4 (including 4) OR Bob’s pick is at least 8? (d) Given that Alice picks 8, what is the probability that...
Alice and Bob visit the gym on Saturday for their hourlong workouts. Alice always arrives between...
Alice and Bob visit the gym on Saturday for their hourlong workouts. Alice always arrives between 2:00 and 3:00 and Bob between 2:30 and 3:30. Assuming their arrival times are drawn independently and uniformly from the specified intervals (i.e. any arrival time in the given window is equally likely), and assuming they each stay for precisely one hour, what is the probability that on any given Saturday there exists a moment in time when all two are present at the...
Each day, two students, Xavier and Yolanda, arrive independently at McDonalds for lunch at a random...
Each day, two students, Xavier and Yolanda, arrive independently at McDonalds for lunch at a random time between noon and 1 p.m. Let X be the time that Xavier arrives (in minutes after 12 p.m.) and Y be the time that Yolanda arrives (in minutes after 12 p.m.). X and Y are independent Uniform(a=0,b=60) random variables. all answers to 3 decimal places a) FInd the joint p.d.f. of X and Y, then find it at f(15,25) b) If both Xavier...
Problem 3. Alice is waiting for a bus at a bus stop. She needs to take...
Problem 3. Alice is waiting for a bus at a bus stop. She needs to take a bus number 10 or 12, and she takes the first suitable bus that arrives. The arrival time of bus 10 is exponential with λ10 = 6/19, and the arrival time of bust 12 is exponential with λ12 = 3/19. Moreover, arrival times of 10 and 12 are independent. What is the probability that Alice will take bus number 10 instead of bus number...
A man and a woman agree to meet at a cafe about noon. If the man...
A man and a woman agree to meet at a cafe about noon. If the man arrives at a time uniformly distributed between 11:35 and 12:10 and if the woman independently arrives at a time uniformly distributed between 11:55 and 12:55, what is the probability that the first to arrive waits no longer than 15 minutes?
Suppose that the time between arrivals of customers at a bank during the​ noon-to-1 p.m. hour...
Suppose that the time between arrivals of customers at a bank during the​ noon-to-1 p.m. hour has a uniform distribution between 0 and 30 seconds. a. What is the probability that the time between the arrivals of two customers will be less than 14 ​seconds? b. What is the probability that the time between the arrivals of two customers will be between 11 and 19 ​seconds? c. What is the probability that the time between the arrivals of two customers...
1. Assume the waiting time at the BMV is uniformly distributed from 10 to 60 minutes,...
1. Assume the waiting time at the BMV is uniformly distributed from 10 to 60 minutes, i.e. X ∼ U ( 10 , 60 )X ∼ U ( 10 , 60 ) What is the expected time waited (mean), and standard deviation for the above uniform variable?   1B) What is the probability that a person at the BMV waits longer than 45 minutes? 1C) What is the probability that an individual waits between 15 and 20 minutes, OR 35 and...
The time between arrivals of taxis at a busy intersection is exponentially distributed with a mean...
The time between arrivals of taxis at a busy intersection is exponentially distributed with a mean of 10 minutes. (i) What is the probability that you wait longer than one hour for a taxi? (ii) Suppose that you have already been waiting for one hour for a taxi. What is the probability that one arrives within the next 10 minutes? (iii) Determine x such that the probability that you wait more than x minutes is 0.10. (iv) Determine x such...
Quiz 4. John's answering machine receives about 7 telephone calls between 8 a.m. and 10 a.m....
Quiz 4. John's answering machine receives about 7 telephone calls between 8 a.m. and 10 a.m. What is the probability that John receives exactly one phone call between 9:00 am and 9:15 am? 5. Bus waiting time is uniformly distributed with the shortest and the longest waiting times being 9 and 21 minutes respectively. What is the standard deviation of the average waiting time of 46 passenger 6. The amount of time spouses shop for anniversary cards can be modeled...
Sepsis Case Study Review Scenario: At 12:00 noon, Jose Guerrero, a 17 year old high school...
Sepsis Case Study Review Scenario: At 12:00 noon, Jose Guerrero, a 17 year old high school student on the soccer team, arrives at the Emergency Department (ED) a few days after cutting his foot at practice. The area on his foot around the wound has progressively gotten red, tender, hot to the touch, and has some drainage. Today it caused pain when walking and he was feeling weak and had a temperature. His only medical history is a mild case...
ADVERTISEMENT
Need Online Homework Help?

Get Answers For Free
Most questions answered within 1 hours.

Ask a Question
ADVERTISEMENT