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Conditional Distributions of Discrete Random Variables. P(A B)=P(A?B)P(B). We use this same concept for events to define conditional probabilities for random variables.

A conditional distribution is the probability distribution of a random variable, calculated according to the rules of conditional probability after observing the realization of another random variable. Overview.

Conditional probability distributions are useful because we often collect data for two variables (like Gender and Sports Preference) but we're interested in answering questions about probability when we happen to know the value of one of the variables.

If we want to know the probability that a person prefers a certain sport given that they are male, then this is an example of a conditional distribution. The value of one random variable is known (the person is male), but the value of the other random variable is unknown (we don't know their favorite sport).

The marginal distribution describes the likelihood of an event to occur, independent of others, while the conditional distribution describes the likelihood of an event to occur given the outcome of another.

Joint probability is the probability of two events occurring simultaneously. Marginal probability is the probability of an event irrespective of the outcome of another variable. Conditional probability is the probability of one event occurring in the presence of a second event.

A conditional distribution is a distribution of values for one variable that exists when you specify the values of other variables. This type of distribution allows you to assess the dispersal of your variable of interest under specific conditions, hence the name.