All Flashcards
What is the formula for the expected value (mean) of a discrete random variable?
E(X) = \sum x \cdot P(X=x)
What is the formula for the variance of a discrete random variable?
Var(X) = \sum (x - E(X))^2 \cdot P(X=x)
What is the formula for the standard deviation of a discrete random variable?
SD(X) = \sqrt{Var(X)}
Given a probability distribution, how do you calculate E(X)?
Multiply each value of X by its probability and sum the results.
How is standard deviation related to variance?
Standard deviation is the square root of the variance.
What is the definition of a random variable?
A numerical outcome from a random event.
What is the definition of expected value?
The average outcome over many trials; the long-run average.
What is the definition of variance?
A measure of how spread out the values of a random variable are around the mean.
What is the definition of standard deviation?
The square root of the variance; measures spread in the same units as the random variable.
Define a discrete random variable.
A random variable with countable values.
What are the differences between variance and standard deviation?
Variance: Average squared distance from the mean, units are squared. | Standard Deviation: Square root of variance, units are the same as the data.
What are the differences between a parameter and a random variable?
Parameter: Describes a population. | Random Variable: Assigns numerical values to outcomes of random phenomena.
What are the differences between discrete and continuous random variables?
Discrete: Countable values (e.g., number of texts). | Continuous: Any value within a range (e.g., height).
What are the differences between calculating variance and standard deviation?
Variance: Requires summing the squared differences from the mean, weighted by probabilities. | Standard Deviation: Simply taking the square root of the calculated variance.
What are the differences between interpreting variance and standard deviation?
Variance: Indicates the average squared deviation from the mean; harder to directly interpret. | Standard Deviation: Indicates the typical deviation from the mean in original units; easier to interpret in context.