Review 1: Probability for 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 of items or occurrences.

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, expressed as a number between 0 and 1.

Front

What does it mean for probabilities to sum to 1 in a probability distribution?

Back

In a probability distribution, the sum of all probabilities must equal 1, indicating that one of the possible outcomes must occur.

Front

How do you calculate the probability of at least one event occurring?

Back

To find the probability of at least one event occurring, you can subtract the probability of the event not occurring from 1.

Front

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

Back

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

Front

What does the notation P(X = k) represent?

Back

P(X = k) represents the probability that the random variable X takes on the value k.

Front

What is the meaning of the term 'cumulative probability'?

Back

Cumulative probability is the probability that a random variable takes on a value less than or equal to a certain value.

Front

How do you interpret P(X > 1) in a probability distribution?

Back

P(X > 1) represents the probability that the random variable X takes on a value greater than 1.

Front

What is the probability of trapping at least three mice if the probabilities are given?

Back

To find the probability of trapping at least three mice, sum the probabilities of trapping 3, 4, and 5 mice.

Front

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

Back

Calculate the probabilities of getting exactly 4 and exactly 5 correct answers, then sum those probabilities.