Workshop: Discrete Random Variables

Front

What is a discrete random variable?

Back

A discrete random variable is a type of variable that can take on a countable number of distinct values, often representing counts or whole numbers.

Front

What is the probability of getting exactly k successes in n trials?

Back

The probability is given by the formula: P(X = k) = (n choose k) * p^k * (1-p)^(n-k), where p is the probability of success.

Front

What does the term 'binomial distribution' refer to?

Back

A binomial distribution is a probability distribution that summarizes the likelihood of a value taking on two independent outcomes, typically 'success' and 'failure', in a fixed number of trials.

Front

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

Back

The mean (expected value) is calculated as E(X) = Σ [x * P(x)], where x represents the values of the random variable and P(x) is the probability of each value.

Front

What is the difference between binompdf and binomcdf?

Back

binompdf calculates the probability of getting exactly k successes, while binomcdf calculates the cumulative probability of getting at most k successes.

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

What are the conditions for a valid probability distribution?

Back

1. All probabilities must be between 0 and 1. 2. The sum of all probabilities must equal 1.

Front

What does 'at most' mean in probability?

Back

'At most' refers to the maximum number of successes allowed in a probability scenario, including all values less than or equal to that number.

Front

How do you find the probability of getting at least k successes?

Back

To find the probability of getting at least k successes, you can use: P(X ≥ k) = 1 - P(X < k) = 1 - binomcdf(n, p, k-1).

Front

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

Back

Variance is calculated as Var(X) = E(X^2) - [E(X)]^2, where E(X^2) is the expected value of the square of the variable.