Discrete Probability Distributions

Front

What is a discrete probability distribution?

Back

A discrete probability distribution is a statistical distribution that describes the likelihood of each possible outcome of a discrete random variable, where the outcomes are countable.

Front

How do you calculate the expected value of a discrete random variable?

Back

The expected value (E) is calculated by multiplying each possible outcome by its probability and summing all these products: E(X) = Σ [x * P(x)].

Front

What is the mean of a probability distribution?

Back

The mean of a probability distribution is the expected value, representing the average outcome of a random variable.

Front

What is the formula for calculating the mean from a frequency distribution?

Back

Mean = (Σ [x * f]) / N, where x is the value, f is the frequency, and N is the total number of observations.

Front

What does it mean for a distribution to be normally distributed?

Back

A normally distributed variable has a symmetric bell-shaped curve, characterized by its mean and standard deviation, where most observations cluster around the mean.

Front

What is the standard deviation in a probability distribution?

Back

The standard deviation measures the amount of variation or dispersion of a set of values in a probability distribution.

Front

How do you interpret the expected value in a real-world scenario?

Back

The expected value provides a long-term average outcome of a random process, helping to make informed decisions based on probabilities.

Front

What is the significance of the probabilities in a discrete probability distribution?

Back

The probabilities must sum to 1, ensuring that all possible outcomes are accounted for in the distribution.

Front

What is a random variable?

Back

A random variable is a variable whose possible values are numerical outcomes of a random phenomenon.

Front

What is the difference between a discrete and a continuous random variable?

Back

A discrete random variable can take on a countable number of values, while a continuous random variable can take on an infinite number of values within a given range.