A random variable is one whose value is unknown or a function that assigns values to each of an experiment’s outcomes. A random variable can be discrete or continuous.

A probability distribution, usually displayed graphically, shows the relative likelihood of all possible outcomes occurring within a specific time period.

Discrete variable's values are also "disjoint," so we have the gaps in a discrete variable's probability distribution graph. While the formula for the expected value of a discrete variable may seem ...

Explain why probability is important to statistics and data science. See the relationship between conditional and independent events in a statistical experiment. Calculate the expectation and variance ...

The alias method of Walker is a clever, new, fast method for generating random variables from an arbitrary, specified discrete distribution. A simple probabilistic proof is given, in terms of mixtures ...

In all examples of discrete random variables, the probabilities in the probability distribution table give the 'long-term' proportion of times that the random variable assumes each possible value.

Additionally, you will learn about conditional probability, random variables, probability distributions, and real-life applications of probability.

In a number of situations we are faced with the problem of determining efficient estimates of the mean and variance of a distribution specified by (i) a non-zero probability that the variable assumes ...