Math Is Fun Forum

purplera1421

Member

Registered: 2009-10-06

Posts: 3

Probability/Stats Question

Consider a coin for which the probability of obtaining a head on each given toss is 0.3. Suppose that the coin is to be tossed 15 times, and let X denote the number of heads that will be obtained.

a) What prediction of X has the smallest mean square error (MSE)?
b) What prediction of X has the smallest mean absolute error (MAE)?

Now for part a, if I am correct, the prediction of X that has the smallest mean square error is just the variance np(1-p) = 3.15 because this is a binomial distribution with parameters n=15 and p=.3. 

But I am puzzled as to how to find the prediction of X with the smallest mean absolute error.  If anyone could explain, I would really appreciate it!

bobbym

bumpkin

From: Bumpkinland

Registered: 2009-04-12

Posts: 109,606

Re: Probability/Stats Question

Hi purplera1421;

I am not sure you can use the MAE in that manner. Doesn't it represent the differences of the actual data to the predicted data. The easiest way to minimize is for each element of the predicted data to be equal to the actual data. Then you would have an MAE of 0. Maybe p is what you want but I don't see how to use it here.

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