Probability Distribution and Expected Value

Front

What is a probability distribution?

Back

A probability distribution is a mathematical function that provides the probabilities of occurrence of different possible outcomes in an experiment.

Front

Define 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

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

Back

To calculate the expected value, multiply each possible value of the random variable by its probability and sum all these products.

Front

What is the formula for expected value (E(X))?

Back

E(X) = Σ [x * P(x)], where x is a value and P(x) is the probability of x.

Front

What does it mean if the expected value is greater than the mean of a dataset?

Back

It indicates that, on average, the outcomes are skewed towards higher 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, ranging from 0 (impossible) to 1 (certain).

Front

What is a random variable?

Back

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

Front

Explain the difference between discrete and continuous random variables.

Back

Discrete random variables have countable outcomes, while continuous random variables can take any value within a given range.

Front

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

Back

The sum of all probabilities in a probability distribution must equal 1, representing the certainty that one of the outcomes will occur.

Front

How do you find the probability of multiple events occurring?

Back

For independent events, multiply their individual probabilities. For dependent events, adjust the probabilities based on previous outcomes.