Mathematics and Statistics
What to master
FE math and statistics items test mechanics more than theory: descriptive statistics (mean, median, variance, standard deviation, coefficient of variation), probability rules, counting, and the standard distributions - binomial, Poisson, exponential, normal, and t. Know when each applies: binomial = fixed n, two outcomes, constant p; Poisson = counts per interval, with the rate scaled to the interval; exponential = time between Poisson events, mean 1/lambda. Review linear algebra basics (matrix multiplication, determinants, solving systems), calculus (derivatives, maxima/minima, area), and simple numerical methods (Newton-Raphson, trapezoidal rule).
Traps
- Sample vs population denominator (n-1 vs n).
- Poisson rate scaling: 2 defects per 100 ft means an expected 1.0 in 50 ft, not 2.
- Using the normal table for a binomial count without a continuity correction.
- Reading a p-value as "the probability the null hypothesis is true."
- Confidence interval misinterpretation: the interval, not the parameter, is what moves.
- Correlation presented as causation, or R-squared confused with a slope.
Worked example
A machine produces defects at lambda = 3 per hour. Probability of exactly zero defects in a 20-minute window: expected count = 3 x (20/60) = 1.0, so P(0) = e^(-1) = 0.368.
Rule of thumb
Compare variability across unlike units with CV = s/x-bar. For a quick normal check, about 68% of data lies within +/-1 sigma, 95% within +/-2 sigma, 99.7% within +/-3 sigma.