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In probability theory, the law (or formula) of total probability is a fundamental rule relating marginal probabilities to conditional probabilities. It expresses the total probability of an outcome which can be realized via several distinct events , hence the name.
For example, for the array of values [−2, 1, −3, 4, −1, 2, 1, −5, 4], the contiguous subarray with the largest sum is [4, −1, 2, 1], with sum 6. Some properties of this problem are: If the array contains all non-negative numbers, then the problem is trivial; a maximum subarray is the entire array.
Then, a tail event is an event which is probabilistically independent of each finite subset of these random variables. (Note: F {\displaystyle F} belonging to F {\displaystyle {\mathcal {F}}} implies that membership in F {\displaystyle F} is uniquely determined by the values of the X k {\displaystyle X_{k}} , but the latter condition is ...
An infinite series of any rational function of can be reduced to a finite series of polygamma functions, by use of partial fraction decomposition, [8] as explained here. This fact can also be applied to finite series of rational functions, allowing the result to be computed in constant time even when the series contains a large number of terms.
A 24-year-old California man was electrocuted and died while hanging Christmas lights on Thursday, according to officials. Antonio Pascual was hanging Christmas lights the morning of Nov. 21 on a ...
[1] [2] A related result, sometimes called the second Borel–Cantelli lemma, is a partial converse of the first Borel–Cantelli lemma. The lemma states that, under certain conditions, an event will have probability of either zero or one. Accordingly, it is the best-known of a class of similar theorems, known as zero-one laws.
Consuming more than 45% of daily calories after 5 p.m. can contribute to greater risk of type 2 diabetes, cardiovascular problems, and chronic inflammation, a recent study suggests.
Get ready to take home deals on our favorite brands during the Black Friday sale event. There are tons of savings to score already at Kohl's. Get ready to take home deals on our favorite brands ...