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We are given the cumulative partition function of the rainy days in march and july. We have a paper, without the name of the month (but we know it is one of these two), on which 14 rainy days are noted. What is the best guess that you would make about the page, is it for the month of march or july? What is the probability that your guess is wrong?

For the first part, i would say that the paper is from march because $P(X=14) = P(X \le 14) - P(X \le 13)$ and this is maximized if we take the month of march ($P(X=14)= 36,01 - 23,66 = 12,35$). Now how do i calculate the probability that i am wrong? Would it be $1-\frac{12,35}{12,35+ 5,63}$?

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    $\begingroup$ Looks good to me, assuming (reasonably) that "14 are noted" means "exactly 14 are noted". $\endgroup$
    – Ian
    Commented May 18, 2015 at 2:11
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    $\begingroup$ A Bayesian would ask you if you have any a priori reason to prefer March or July. If not—if they are equally likely before your analysis—then your reasoning appears sound. $\endgroup$
    – Brian Tung
    Commented May 18, 2015 at 2:54

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Just to close this question, the approach is fine.

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