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Calculus: An Applied Approach (Min...

10th Edition
Ron Larson
ISBN: 9781305860919

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Calculus: An Applied Approach (Min...

10th Edition
Ron Larson
ISBN: 9781305860919
Textbook Problem
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Transportation The arrival time t (in minutes) of a bus at a bus stop is uniformly distributed between 10:00 a.m. and 10:10 a.m.

(a) Find the probability density function for the random variable t.

(b) Find the mean and standard deviation of the arrival time.

(c) What is the probability that you will miss the bus if you arrive at the bus stop at 10:03 a.m.?

(a)

To determine

To calculate: The probability density function for the random variable t, if the time of arrival is t (in minutes) of a bus stop is uniformly distributed between 10:00 A.M. and 10:10 A.M.

Explanation

Given information:

The time of arrival is t (in minutes) of a bus stop is uniformly distributed between 10:00 A.M. and 10:10 A.M.

Formula used:

The uniform probability density function is,

f(t)=1ba,  atb

Calculation:

The arrival time is t,

Consider a function as f with respect to t, and the time distributed as uniformly between 10:00 A.M. and 10:10 A.M.

The time distributed as uniformly between 10:00 A.M. and 10:10 A.M.

For time 10:00 A.M. t=0 as a lower limit and for time 10:10 A

(b)

To determine

To calculate: The mean and standard deviation of the arrival time t of a bus stop is uniformly distributed between 10:00 A.M. and 10:10 A.M.

(c)

To determine

To calculate: The probability that to miss the bus if your arrival time at the bus stop is 10:03 A.M.

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