Explain the concept of sampling variability.
The extent to which sample statistics vary from sample to sample.
Explain the concept of the Central Limit Theorem (CLT).
The CLT states that the sampling distribution of the sample mean approaches a normal distribution as the sample size increases, regardless of the population's distribution.
Explain the concept of standard error.
Standard error measures the variability of the sample statistic. It is the standard deviation of the sampling distribution.
Explain the concept of population parameters.
Population parameters are fixed values that describe characteristics of an entire population, such as the population mean ($\mu$) or population standard deviation ($\sigma$).
Explain the concept of sample statistics.
Sample statistics are estimates of population parameters calculated from a sample, such as the sample mean ($\bar{x}$) or sample standard deviation (s).
What are the differences between discrete and continuous random variables?
Discrete: Finite or countable values, e.g., number of students | Continuous: Any value within a range, e.g., height.
What are the differences between population parameters and sample statistics?
Parameters: Describe populations, fixed values | Statistics: Describe samples, estimates of parameters.
What is the formula for the mean (expected value) of a discrete random variable?
$E(X) = \sum x_i \cdot P(x_i)$
What is the formula for the standard deviation of a discrete random variable?
$\sigma = \sqrt{\sum (x_i - \mu)^2 \cdot P(x_i)}$
