Question

In: Statistics and Probability

You arrive at the train station between 7:20 am and 7:30 am, uniformly. The train arrives...

You arrive at the train station between 7:20 am and 7:30 am, uniformly. The train arrives every 8 minutes starting from 7:00 am. Let Y be the waiting time. Please compute the pdf of Y.

Expert Solution

SOLUTION:

From given data,

You arrive at the train station between 7:20 am and 7:30 am, uniformly. The train arrives every 8 minutes starting from 7:00 am. Let Y be the waiting time. Please compute the pdf of Y.

Where,

The train station between 7:20 am and 7:30 am.

The train arrives every 8 minutes starting from 7:00 am.

Let Y be the waiting time. (this will be in minutes)

Y = - X + 24 , 20 < X < 24

Y = - X + 30 , 25 < X < 30

X follows uniform distribution in the range [20 , 30]

f(X) =1/(30-20)= 1/10 , 20 < X < 30

f(X) = 0 , else

and

f(Y) = f(X) ( X / Y )

f(Y) = (1/10) ( X / Y (24-Y))

f(Y) = - 1/10 , 20 < X < 30

the pdf of Y is - 1/10 , 20 < X < 30

orchestra answered 1 year ago

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