How can I solve this uniform distribution question?

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Homework Help Overview

The discussion revolves around a conditional probability question related to a uniform distribution, specifically focusing on the waiting time in a queue. Participants are analyzing the implications of given conditions on the probability calculations.

Discussion Character

  • Conceptual clarification, Assumption checking

Approaches and Questions Raised

  • Participants are exploring the correct interpretation of conditional probabilities, particularly questioning the transition from P(X>8) and P(X=5) to P(X>8) / P(X>=5). There is also a discussion about the meaning of the random variable X in the context of waiting time.

Discussion Status

The discussion is ongoing, with participants providing insights and questioning assumptions about the uniform distribution and the implications of the waiting time. Some guidance has been offered regarding the correct formulation of the probabilities, but no consensus has been reached yet.

Contextual Notes

There is a focus on the specific conditions of the problem, including the fact that the participant has already waited 5 minutes, which influences the interpretation of the random variable X. The constraints of the uniform distribution from 0 to 10 are also noted.

jsmith613
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Homework Statement


http://www.xtremepapers.com/Edexcel/Advanced%20Level/Mathematics/Subject%20Sorted/S2/S2%202008-06.pdf

Question 1(d)

Homework Equations



The Attempt at a Solution


So I know this is a conditional probability question.
Now I would have said
P(X>8) / P(X=5)
because it is probability I will NOT be served (i.e: time is greater than 8 mins) given I have already waited 5 mins
this gives me infinity because x/0 = inifinty

How do I approach this question?
 
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jsmith613 said:

Homework Statement


http://www.xtremepapers.com/Edexcel/Advanced%20Level/Mathematics/Subject%20Sorted/S2/S2%202008-06.pdf

Question 1(d)

Homework Equations



The Attempt at a Solution


So I know this is a conditional probability question.
Now I would have said
P(X>8) / P(X=5)
because it is probability I will NOT be served (i.e: time is greater than 8 mins) given I have already waited 5 mins
this gives me infinity because x/0 = inifinty

How do I approach this question?

No: because she has already waited 5 minutes, we know that X >= 5. You need P{X > 8}/P{X >= 5}.

RGV
 
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see that's the prob I can't see why its x≥5 because she has waited 5 mins (x=5)
X = the amount of time Jean waits in the queue?
 
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jsmith613 said:
see that's the prob I can't see why its x≥5 because she has waited 5 mins (x=5)
X = the amount of time Jean waits in the queue?

X = amount of time that Jean would spend in the queue if she did not have to leave before being served; this is the random quantity representing the times she did spend in the queue on every day in the past. So, X is uniform from 0 to 10. On this one occasion we observe that after 5 minutes she is still in the queue, so on this one occasion, X >= 5. (X is not exactly equal to 5, because if it was she would not need to wait any longer; and, of course, X is not less than 5.) On this one occasion, the amount of time she spends in the queue is X (if X <= 8) and is 8 (if X > 8).
 
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