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Answered: - Earlier, we used the uniform distribution between 0 and m


Earlier, we used the uniform distribution between 0 and ? mile to model the distance from where a car would breakdown on the Pennsylvania Turnpike and the nearest call box. But if we are trying to model howfar an actual driver might have to walk we have to consider other factors to make the model morerealistic:

1) A driver wouldn?t always know which direction they should walk to get to the nearestcall-box depending on the probability that he/she had noticed how far back the last onewas, and

2) When you break down very close to a call-box (say within 0.05 miles) you would be ableto see it and thus know which direction to walk for sure.

a) With these two new issues taken into account, Find the cdf and pdf of Y = the distance adriver would walk to get to a call-box when they break down?

b) What is E(Y) and SD(Y) under the new model? (compare them to the corresponding answersunder the original model)?


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Let X be as in the old model, distance where car would break down in [0.0.5].

 

pdf of X is f(x)=2, x in [0,0.5]

 

Let Y = distance driver would walk to a call-box

 

Observe that Y is...

 


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