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This section explores random variables and their classifications. A random variable (RV) associates numbers with outcomes in a sample space, with Bernoulli RVs specifically taking values of 0 or 1. Discrete RVs can have finite or countable infinite values, while continuous RVs cover entire intervals on a number line. The probability distribution, or probability mass function (pmf) for discrete RVs, maps values to probabilities, and the cumulative distribution function (cdf) calculates the likelihood of observing values up to a certain point.
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Ch3.1-3.2 For a given sample space S of some experiment, a random variable is any rule that associates a number with each outcome in S . Any random variable whose only possible values are 0 and 1 is called a Bernoulli random variable. A discrete random variable is an RV whose possible values either constitute a finite set or else can listed in an infinite sequence. A random variable is continuous if its set of possible values consists of an entire interval on a number line. Ch3.1-3.2
3.1-3.2 The probability distribution or probability mass function (pmf) of a discrete RV is defined for every number x by p(x) = S The cumulative distribution function (cdf) F(x) of a discrete RV variable X with pmfp(x) is defined for every number by For any number x, F(x) is the probability that the observed value of X will be at most x. Ch3.1-3.2
3.1-3.2 Proposition: For any two numbers a and b with “a–” represents the largest possible X value that is strictly less than a. Note: For integers Ch3.1-3.2
