Discrete Probability Distributions

Front

What is a discrete probability distribution?

Back

A discrete probability distribution is a statistical distribution that describes the likelihood of obtaining the possible values that a discrete random variable can take.

Front

What is a random variable?

Back

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

Front

Define the term 'probability'.

Back

Probability is a measure of the likelihood that an event will occur, expressed as a number between 0 and 1.

Front

What is the formula for calculating the probability of exactly k successes in n trials?

Back

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

Front

What does 'n choose k' mean in probability?

Back

'n choose k' (denoted as C(n, k) or nCk) is the number of ways to choose k successes from n trials, calculated as n! / (k!(n-k)!).

Front

What is the probability of getting at least 4 correct answers on a 5-question true-false quiz?

Back

The probability of getting at least 4 correct answers is the sum of the probabilities of getting exactly 4 and exactly 5 correct answers.

Front

How do you calculate the probability of getting exactly 4 correct answers on a 5-question quiz?

Back

P(X = 4) = C(5, 4) * (0.5)^4 * (0.5)^(5-4) = 5 * 0.0625 * 0.5 = 0.15625.

Front

What is the probability of getting exactly 5 correct answers on a 5-question quiz?

Back

P(X = 5) = C(5, 5) * (0.5)^5 * (0.5)^(5-5) = 1 * 0.03125 * 1 = 0.03125.

Front

What is the total probability of getting at least 4 correct answers?

Back

Total probability = P(X = 4) + P(X = 5) = 0.15625 + 0.03125 = 0.1875.

Front

What is the expected value of a discrete random variable?

Back

The expected value is the long-term average value of repetitions of the experiment it represents, calculated as E(X) = Σ [x * P(x)].