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In the unit on Minterms , we show how to use minterm probabilities and minterm vectors to calculate probabilities of Boolean combinations of events. In Independence of Events we show that in theindependent case, we may calculate all minterm probabilities from the probabilities of the basic events. While these calculations are straightforward, they may be tedious andsubject to errors. Fortunately, in this case we have an m-function minprob which calculates all minterm probabilities from the probabilities of the basic or generating sets. This function uses the m-function mintable to set upthe patterns of p 's and q 's for the various minterms and then takes the products to obtain the set of minterm probabilities.
>>pm = minprob(0.1*[4 7 6])pm = 0.0720 0.1080 0.1680 0.2520 0.0480 0.0720 0.1120 0.1680
It may be desirable to arrange these as on a minterm map. For this we have an m-function minmap which reshapes the row matrix $pm$ , as follows:
>>t = minmap(pm)
t = 0.0720 0.1680 0.0480 0.11200.1080 0.2520 0.0720 0.1680
Probability of occurrence of k of n independent events
In Example 2, we show how to use the m-functions mintable and csort to obtain the probability of the occurrence of k of n events, when minterm probabilities are available. In the case of an independent class, the minterm probabilities are calculated easilyby minprob, It is only necessary to specify the probabilities for the n basic events and the numbers k of events. The size of the class, hence the mintable, is determined, and the minterm probabilities are calculated by minprob. We have twouseful m-functions. If P is a matrix of the n individual event probabilities, and k is a matrix of integers less than or equal to n , then
$\text{function}y=\mathrm{ikn}(P,k)$ calculates individual probabilities that $k$ of $n$ occur
$\text{function}y=\mathrm{ckn}(P,k)$ calculates the probabilities that $k$ or more occur
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