Conditional probability question

In summary, the person is asking for help in calculating the conditional probability function of the second journey time given the first journey time. They provide a link to the data and mention the importance of grounding the relationship between the variables in physical knowledge. They suggest using the data to construct a family of probability distributions for the different variables, such as a normal distribution with variances related to their means.
  • #1
bradyj7
122
0
Hi there,

I have the journey times of 2 journeys. Would somebody be able to show me by way of example how to calculate the conditional probability function of the second journey time given the first journey time?

https://dl.dropbox.com/u/54057365/All/jt.JPG

Appreciate your help

Thanks

John
 
Last edited by a moderator:
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  • #2
You cannot deduce such a probability without constructing some relationship between the underlying variables. Wherever possible, this should be grounded in the knowledge of the physical system, not just abstract datapoints. In the present case, would I be right in guessing that the two times for a journey are effectively samples of the same r.v.? If so, you need to use the data to construct a family of probability distributions for these different r.v.s. E.g., they could be normally distributed with variances functionally related to their means. (But normal dist is likely not a good bet since they cannot go negative.)
 

1. What is conditional probability?

Conditional probability is a mathematical concept that represents the likelihood of an event occurring given that another event has already occurred. It is used to calculate the probability of one event happening, based on the knowledge of another related event.

2. How is conditional probability calculated?

Conditional probability is calculated by dividing the probability of the joint occurrence of two events by the probability of the first event. This can be represented by the formula P(A|B) = P(A and B) / P(B), where P(A|B) is the conditional probability of A given B, P(A and B) is the probability of both A and B occurring, and P(B) is the probability of B occurring.

3. What is the difference between conditional probability and independent probability?

Conditional probability takes into account the occurrence of a previous event, whereas independent probability assumes that events are not affected by each other. In conditional probability, the outcome of one event affects the probability of the other event occurring, while in independent probability, the outcome of one event has no impact on the other event.

4. Can conditional probability be greater than 1?

No, conditional probability cannot be greater than 1. This is because the probability of an event occurring cannot exceed 100% or the certainty of it happening. If the conditional probability is calculated to be greater than 1, it is likely that a mistake was made in the calculation.

5. What are some real-world applications of conditional probability?

Conditional probability is used in many fields, including statistics, finance, and science. Some common applications include predicting stock market trends, analyzing medical diagnoses, and determining the likelihood of a disease occurring based on risk factors. It is also used in everyday situations, such as predicting the chances of rain based on weather conditions.

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