14.The time between successive arrivals of the planes to a busy airport is random variable whichfollows exponential distribution. It was observed that on average planes arrive to the airport0.2 arrivalsevery five minutes (1/2=5 min) and average number of arrivals in one minute is λ=-1 mina. The probability that the time between successive arrivals is less than 5 minutes isb. The probability that the time between successive arrivals is more than 10 minutes isc. The probability that the time between successive arrivals is between 15 and 20 minutes isAssume that the time between successive arrivals of the planes is exponential random variabledenoted by Y.Show some work to answer questions a, b. and c.

On average planes arrive to the airport every five minutes. That is .Average number of arrivals in…

Answered: The time between successive arrivals of…

A First Course in Probability (10th Edition)

10th Edition

ISBN:9780134753119

Author:Sheldon Ross

Publisher:Sheldon Ross

Chapter1: Combinatorial Analysis

Section: Chapter Questions

Problem 1.1P: a. How many different 7-place license plates are possible if the first 2 places are for letters and...

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A person arrives at the side of a single lane, one way street as a car passes by. Consider this time as time 0. There is no traffic lights and no pedestrian lanes in the nearby area. He stands there watching cars pass by. The number of cars to pass by within a period of time cane be modeled using a poison distribution. Suppose the cars pass by the person at a rate of 4.5 cars per minute. Assume that the cars pass by instantaneously. what is the probability that no cars pass by him within a 2 minute window b) if the person had to guess how many cars would pass by in the next five minutes, what number should he guess? Why? c) what is the distribution for the time until the first car passes by him(time is continuous). What is the expected time until the first car passes by him?
8 Julia is waiting for either of the two buses to her destination, and waiting times for those two different buses follow independent exponential distributions with mean 3 minutes and 7 minutes. Assuming she would get on the bus that comes first, what is her expected waiting time?
Assume the below life table was constructed from following individuals who were diagnosed with a slow-progressing form of prostate cancer and decided not to receive treatment of any form. Calculate the survival probability at year 1 using the Kaplan-Meir approach and interpret the results. Time in Years Number at Risk, Nt Number of Deaths, Dt Number Censored, Ct Survival Probability 0 20 1 1 20 3 2 17 1 3 16 2 1 The probability of surviving 1 year after being diagnosed with a slow-progressing form of prostate cancer is .85. The probability of surviving 1 year after being diagnosed with a slow-progressing form of prostate cancer is .85 for the individuals being followed in this study. The probability of surviving 1 year after being diagnosed with a slow-progressing form of prostate cancer is .85 for individuals who decided against all forms of treatment. The probability of surviving 1 year after being…
Anomal distribution has of mu = 50 with sigma = 6 6. one score randomly selected from this distributionwhich is the probability that the score will be greater than X = 46
The times between arrivals in a queue follow an exponential distribution with a rate of 1. Check the incorrect alternative: a) 50% of arrivals will take place before 1 minute. b) If the times between arrivals are exponentially distributed with a rate equal to 1, then arrivals occur according to a Poisson distribution with an average equal to 1. c) Times between arrivals are independent. d) The variance of the times between arrivals is equal to 1. e) There is an average of one arrival every minute.
6.2/3
4) What number of drones N makes your second-morning observations as likely as possible?5) Assuming again that the probability that N = n is proportional to the probability of observing this specificdata on the second day, find again the smallest nmax so that P (N ≤ nmax) = 0.95.
Question 7 According to the data, the weight of a randomly selected checked-in luggage has a normal distribution with a mean of 51 lbs and a standard deviation of 9 lbs. Let X be the weight of a randomly selected checked-in luggage and let S be the total weight of a random sample of size 33. 1. Describe the probability distribution of X and state its parameters and o: X~ Select an answer (μ = Select an answer unknown X² B N T 2. Use the Central Limit Theorem and find the probability that the weight of a randomly selected checked-in luggage is less than 61 lbs. (Round the answer to 4 decimal places) Check-In Select an answer Select an answer the original population is normally distributed the sample size is large (n>30) although the distribution of the original population is unknown the sample size is small (n<30) and the distribution of the original population is unknown the distribution of the original population is unknown S~ Select an answer (s= Select an answer σ= to describe the…
An experiment consists of flipping a weighted coin with Pr[H]=0.6. The experiment ends when either heads is flipped 3 times or tails is flipped. What is the probability that heads was flipped at least once given the coin was flipped at most two times?
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