The waiting times between a subway departure schedule and the arrival of a passenger are uniformly distributed between0 and8 minutes. Find the probability that a randomly selected passenger has a waiting time greater than 3.25 minutes.Find the probability that a randomly selected passenger has a waiting timegreater than 3.25 minutes.

Question
Asked Oct 19, 2019

The waiting times between a subway departure schedule and the arrival of a passenger are uniformly distributed between

0
 

and

8
 

minutes. Find the probability that a randomly selected passenger has a waiting time greater than 3.25 minutes.

Find the probability that a randomly selected passenger has a waiting time
greater than 3.25 minutes.
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Expert Answer

Step 1

Continuous uniform distribution:

A random variable X is said to have the rectangular distribution or the continuous distribution with parameters (a, b), if a and b are the minimum and maximum possible values of X respectively, such that the probabilities of getting X in all equal intervals within (a, b) are equal. The probability density function (PDF) of the uniformly distributed random variable with parameters (a, b) is:

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Step 2

The distribution in this case:

Let X denotes waiting times between a subway departure schedule and the arrival of a passenger. Here, the random variable X is ...

1
0x 8
f (x)8-0
(0,
That is
otherwise
0sx8
f(x)
0, otherwise.
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Image Transcriptionclose

1 0x 8 f (x)8-0 (0, That is otherwise 0sx8 f(x) 0, otherwise.

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