Probability and Statistics
Probability and statistics quantify uncertainty and support data-driven decisions. The FE tests basic probability, descriptive statistics, distributions, and estimation.
Probability Basics
Probability is favorable outcomes divided by total equally likely outcomes. For independent events, probabilities multiply; for mutually exclusive events, they add. Rolling two dice, for example, gives 36 outcomes with a most-likely sum of 7.
Descriptive Statistics
The mean locates the center of data; variance and standard deviation measure spread. The SAMPLE standard deviation divides the summed squared deviations by (n - 1), giving an unbiased estimate of the population value.
Distributions and Estimation
The normal distribution models many natural phenomena; z-scores standardize values. Confidence intervals and hypothesis tests use sample statistics to draw conclusions about populations, quantifying the risk of error.