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Two or more events are independent if the occurrence of one event does not influence the occurrence of the other event(s). Let us put this in annotations:

A cumulative distribution function, \(F(x)\), gives the probability that the random variable \(X\) is less than or equal to \(x\): $$ P(X ≤ x) $$ By analogy, this concept is very similar to the cumulative relative frequency.

Unconditional Probability Unconditional probability (also known as marginal probability) is simply the probability that the occurrence of an event does not, in any way, depend on any other preceding events. In other words, unconditional probabilities are not conditioned on the…

Defining properties of a probability refers to the rules that constitute any given probability. These are:

Odds for and against an event represent a ratio of the desired outcomes versus the field. In other words, the odds for an event are the ratio of the number of ways the event can occur to the number of…

Odds for and against an event represent a ratio of the desired outcomes versus the field. In other words, the odds for an event are the ratio of the number of ways the event can occur to the number of…

Defining properties of a probability refer to the rules that constitute any given probability. These are:

Expected Value The expected value of a random variable is simply the average of the possible outcomes of that variable, taking into account the probability weights. Thus: $$ E\left( X \right) =\sum _{ i=1 }^{ n }{ { X }_{…

Probability is a measure of the likelihood that something will happen. We usually express probabilities as percentages, from 0% (impossible to happen) to 100% (guaranteed). We can express almost any event as a probability. For instance, we can gauge the…