Prob Dist & Binomial

Front

What is the mean of a probability distribution?

Back

The mean (or expected value) of a probability distribution is the sum of all possible values, each multiplied by its probability. It represents the average outcome.

Front

How do you denote the probability of a random variable X being greater than or equal to a certain value?

Back

P(X ≥ k) denotes the probability that the random variable X is greater than or equal to 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 calculated using the binomial probability formula. For 4 correct answers, P(X=4) and for 5 correct answers, P(X=5) are summed.

Front

What is a probability distribution?

Back

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

Front

What is the condition for a valid probability distribution?

Back

A valid probability distribution must satisfy two conditions: 1) All probabilities must be between 0 and 1, and 2) The sum of all probabilities must equal 1.

Front

How do you find the missing probability in a probability distribution?

Back

To find the missing probability, subtract the sum of the known probabilities from 1.

Front

What does P(X < k) represent?

Back

P(X < k) represents the probability that the random variable X takes on a value less than k.

Front

What is the binomial probability formula?

Back

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

Front

What is the significance of the standard deviation in a probability distribution?

Back

The standard deviation measures the amount of variation or dispersion in a set of values. In a probability distribution, it indicates how spread out the values are around the mean.

Front

What does it mean if a probability distribution is skewed?

Back

A skewed probability distribution is one where the probabilities are not evenly distributed around the mean, leading to a longer tail on one side.