Discrete Probability Distributions

Front

What is a discrete probability distribution?

Back

A discrete probability distribution is a statistical distribution that describes the likelihood of outcomes of a discrete random variable, which can take on a countable number of values.

Front

How do you calculate the mean of a discrete probability distribution?

Back

The mean (expected value) is calculated by multiplying each possible value by its probability and summing the results: E(X) = Σ [x * P(x)].

Front

What is the expected value in probability?

Back

The expected value is the long-term average or mean of a random variable, calculated as the sum of all possible values, each multiplied by its probability.

Front

Define variance in the context of probability distributions.

Back

Variance measures the spread of a set of values in a probability distribution, calculated as the average of the squared differences from the mean.

Front

What is the formula for calculating variance of a discrete random variable?

Back

Variance (σ²) = Σ [(x - μ)² * P(x)], where μ is the mean.

Front

Explain the concept of standard deviation in probability.

Back

Standard deviation is the square root of the variance and provides a measure of the amount of variation or dispersion in a set of values.

Front

What is the probability of an event?

Back

The probability of an event is a measure of the likelihood that the event will occur, expressed as a number between 0 (impossible) and 1 (certain).

Front

How do you find the probability of multiple independent events occurring?

Back

For independent events, the probability of all events occurring is the product of their individual probabilities: P(A and B) = P(A) * P(B).

Front

What is a probability mass function (PMF)?

Back

A probability mass function is a function that gives the probability that a discrete random variable is exactly equal to some value.

Front

What does it mean for a distribution to be binomial?

Back

A binomial distribution represents the number of successes in a fixed number of independent Bernoulli trials, each with the same probability of success.