Mean and variance of his time of arrival in the city

Assignment Help Basic Statistics

Reference no: EM131833174

Consider a person who commutes to the city from a suburb by train. He is accustomed to leaving his home between 7:30 and 8:00 A.M. The drive to the railroad station takes between 20 and 30 minutes. Assume that the departure time and length of trip are independent random variables, each uniformly distributed over their respective intervals. There are 3 trains that he can take, which leave the station and arrive in the city precisely on time. The first train leaves at 8:05 A.M. and arrives at 8:40 A.M., the second leaves at 8:25 A.M. and arrives at 8:55 A.M., the third leaves at 9:00 A.M. and arrives at 9:43 A.M.

(i) Find the mean and variance of his time of arrival in the city.

(ii) Find the mean and variance of his time of arrival under the assumption that he leaves his home between 7:30 and 7:55 A.M.

Reference no: EM131833174

Questions Cloud

Find the mean and variance of the number of deaths : Find the mean and variance of the number of deaths within a year among 20,000 men of this age.

How much should the man be willing to pay for a ticket : How much should the man be willing to pay for a ticket in this lottery?

What is its mean and variance : The amount of money in the red purse at the end of this experiment is a random variable. What is its mean and variance?

Probability and its engineering uses : Probability and Its Engineering Uses, Van Nostrand, New York, 1928, pp. 194-199.)

Mean and variance of his time of arrival in the city : (i) Find the mean and variance of his time of arrival in the city.

Find the mean and variance of the number of games : Find the mean and variance of the number of games required to conclude the series. (Use exercise 3.26 of Chapter 3.)

Experiment that consists of n players independently : Consider an experiment that consists of N players independently tossing fair coins. Let A be the event that there is an "odd" man (that is, either exactly

Largest number in the sample : Let a sample of size 3 be drawn with replacement (without replacement) from the urn and let X be the largest number in the sample.

Find the mean and variance : Let X be N(m, s2). Find the mean and variance of (i) |X|, (ii) |X - c| where (a) c is a given constant, (b) s = |1| = C = 1, (c) a = m = 1, c = 2.

User Account

All Pages