P(X = 1) = 1/6 (if we only throw the die once, we get a 6 on our first throw. Let X be the random variable representing the number of times we throw the die. Find the probability density function for the number times we throw the die. In the above example, P(X = x) = 3C x / (2) 3 (see permutations and combinations for the meaning of 3C x).Ī die is thrown repeatedly until a 6 is obtained. Quite often, the probability density function will be given to you in terms of x. In the above example, we could therefore have written: Here, P(X = 0) = 1/8 (the probability that we throw no heads is 1/8 ). So P(X = 0) means "the probability that no heads are thrown". So in the above example, X represents the number of heads that we throw. The random variable (r.v.) X is the event that we are considering. The usual notation that is used is P(X = x) = something. Put simply, it is a function which tells you the probability of certain events occurring.
The probability density function (p.d.f.) of X (or probability mass function) is a function which allocates probabilities. The variable is said to be random if the sum of the probabilities is one. In this example, the number of heads can only take 4 values (0, 1, 2, 3) and so the variable is discrete. The probabilities of each of these possibilities can be tabulated as shown:Ī discrete variable is a variable which can only take a countable number of values.
This section covers Discrete Random Variables, probability distribution, Cumulative Distribution Function and Probability Density Function.Ī probability distribution is a table of values showing the probabilities of various outcomes of an experiment.įor example, if a coin is tossed three times, the number of heads obtained can be 0, 1, 2 or 3.
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