Flashcard 9: 6.1-6.2

Front

What is the formula for calculating the expected value (mean) of a random variable?

Back

The expected value (mean) of a random variable X is calculated using the formula: E(X) = Σ [x * P(x)], where x represents the value of the random variable and P(x) is the probability of x.

Front

What is the standard deviation and why is it important in statistics?

Back

Standard deviation is a measure of the amount of variation or dispersion in a set of values. It is important because it provides insight into how spread out the values are around the mean.

Front

How do you calculate the standard deviation of a discrete random variable?

Back

To calculate the standard deviation of a discrete random variable, use the formula: σ = √(Σ [(x - μ)² * P(x)]), where μ is the expected value.

Front

What does it mean for a probability distribution to be normal?

Back

A normal probability distribution is a continuous probability distribution that is symmetric about the mean, showing that data near the mean are more frequent in occurrence than data far from the mean.

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 (impossible event) and 1 (certain event).

Front

What is the concept of 'at most' in probability?

Back

'At most' refers to the maximum number of occurrences of an event that can happen. For example, 'at most one lawn mowed' means zero or one lawn can be mowed.

Front

What does 'at least' mean in probability?

Back

'At least' refers to the minimum number of occurrences of an event that can happen. For example, 'at least one lawn mowed' means one or more lawns can be mowed.

Front

How do you interpret a probability of 0.6?

Back

A probability of 0.6 means there is a 60% chance that the event will occur, indicating it is more likely to happen than not.

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 is the significance of the mean in a probability distribution?

Back

The mean is the average value of a probability distribution and represents the center of the distribution, indicating where most values are concentrated.