A discrete probability distribution for a random variable X̅ is given. Use the given distributio

step 1 First, we list the distribution of the random variable. XI can take the value of 1, 2, 3, and 4,

A discrete probability distribution for a random variable X̅...

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Key Concepts

Discrete Probability Distribution

A discrete probability distribution assigns a probability to each possible outcome of a discrete random variable. It provides a complete description of the probability structure of the random variable, where the sum of all probabilities is equal to one.

Probability Mass Function

The probability mass function (PMF) is a function that gives the probability that a discrete random variable is exactly equal to some value. It serves as the fundamental building block for calculating probabilities over events and for computing expectations.

Event Probability Calculation

Calculating the probability of an event in the context of a discrete random variable involves summing the probabilities (as given by the PMF) over all outcomes that satisfy the event's condition. This method is used to determine probabilities such as P(X ? 2) by adding probabilities for all qualifying outcomes.

Expected Value

The expected value, or expectation, of a random variable is a measure of its central tendency, calculated by summing the products of each outcome and its corresponding probability. It provides an average or mean value that one would expect if the experiment were repeated many times.

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