we discussed two ways to use probability density functions (PDFs). The first ass

Question

we discussed two ways to use probability density functions (PDFs). The first assumes we know the parameters of the distribution, and we wish to estimate the probability of an outcome. The second assumes we have observed outcomes, and want to estimate the parameters. Using some example (this can be as simple as coin flipping or cars through a toll booth), illustrate the difference between these two ways of using PDFs, and explain why in social science we’re nearly always in the second situation. (Hint: This is the difference between PDFs and Likelihood functions, if that helps.)

Explanation / Answer

Let's say we need to estimate the number of car accidents happening. From the past data it is know that number of accidents follows poisson distribution with some mean say lambda.

We wish to predict the number of accidents that can happen in a week to understand how much equipment a newly constructed hospital needs for optimal use. This way we can easily understand if it follows some distribution

Now lets say a coin is flipped and to know whether it is bias or not we might need to find the parameter, p which is the probability of heads turning up assumed to be success. Now we conduct lot of experiments and do it to find whether it is bias.

The reason we use the second one more often is that, sometimes the old data is not there and we dont know the distribution it follows. secondly, the distribution can be dynamic with time. So if we use the same distribition we might get wrong results. so we’re nearly always in the second situation.

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