Unit 6 Discrete Variable Distribution Test

Front

What is a normal random variable?

Back

A normal random variable is a type of continuous random variable that has a bell-shaped probability distribution, defined by its mean (average) and standard deviation (spread).

Front

How do you calculate the probability of a normal random variable falling within a certain range?

Back

Use the Z-score formula: Z = (X - μ) / σ, where X is the value, μ is the mean, and σ is the standard deviation. Then, refer to the standard normal distribution table.

Front

What is the mean in a probability distribution?

Back

The mean is the average value of a random variable, representing the center of the distribution.

Front

What is standard deviation in a probability distribution?

Back

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

Front

What is the probability of at least k successes in a binomial distribution?

Back

Calculate the cumulative probability of getting k-1 successes and subtract from 1: P(X ≥ k) = 1 - P(X < k).

Front

What is a binomial distribution?

Back

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

Front

What is the formula for the expected value of a discrete random variable?

Back

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

Front

What is the expected value of a game?

Back

The expected value is the average amount one can expect to win or lose per game played, calculated by weighing each outcome by its probability.

Front

What is the probability of rolling a specific number on a fair die?

Back

The probability of rolling a specific number on a fair die is 1/6, since there are 6 equally likely outcomes.

Front

What is the concept of 'first success' in probability?

Back

The 'first success' refers to the scenario in a sequence of Bernoulli trials where the first occurrence of a success happens at a specific trial.