Tags: #◇Computer Science #◇STT101A #◇Probability and Statistics #◇Reviewer #◇Finals

STT101A Comprehensive Finals Reviewer

◇Overview

This reviewer consolidates Foundations of Probability and Statistical Inference (STT101A). Core areas include sample spaces, combinatorial counting, probability axioms, conditional probability, Law of Total Probability, Bayes' Formula, discrete random variables (Binomial, Poisson, Geometric), continuous random variables (Normal, Exponential), Central Limit Theorem, confidence intervals, and hypothesis testing ( $z$ -test vs $t$ -test, Type I and II errors, $p$ -values).

◇1. Master Formula & Distribution Matrix

Distribution / Formula	PDF / PMF $P(X = x)$	Mean $E[X]$	Variance $\text{Var}(X)$	Notes / Conditions
Binomial $B(n, p)$	$\binom{n}{x} p^x (1-p)^{n-x}$	$n p$	$n p (1-p)$	$n$ independent Bernoulli trials with probability $p$
Poisson $\text{Pois}(\lambda)$	$\frac{e^{-\lambda} \lambda^x}{x!}$	$\lambda$	$\lambda$	Rare events in continuous interval
Normal $N(\mu, \sigma^2)$	$\frac{1}{\sigma\sqrt{2\pi}} e^{-\frac{(x-\mu)^2}{2\sigma^2}}$	$\mu$	$\sigma^2$	Standard normal $Z = \frac{X - \mu}{\sigma} \sim N(0, 1)$
Bayes' Formula	$P(A_i \mid B) = \frac{P(B \mid A_i) P(A_i)}{\sum_{j} P(B \mid A_j) P(A_j)}$	N/A	N/A	Updates prior $P(A_i)$ to posterior $P(A_i \mid B)$
Sample Mean Distribution	$\bar{X} \sim N\left(\mu, \frac{\sigma^2}{n}\right)$	$\mu$	$\frac{\sigma^2}{n}$	Standard Error $SE = \frac{\sigma}{\sqrt{n}}$ (Central Limit Theorem)

◇2. Hypothesis Testing Decision Matrix

Type I vs Type II Errors

Type I Error ( $\alpha$ ): Rejecting $H_0$ when $H_0$ is actually true (False Positive).
Type II Error ( $\beta$ ): Failing to reject $H_0$ when $H_0$ is false (False Negative).
Statistical Power: $1 - \beta$ (Probability of correctly rejecting a false null hypothesis).

◇3. High-Yield Exam Checklist

When using $t$ -test, did you use degrees of freedom $df = n - 1$ ?
For a two-tailed test at significance level $\alpha = 0.05$ , is the critical region in each tail $\alpha / 2 = 0.025$ ? YES ( $Z_{crit} = \pm 1.96$ ).
Did you remember: If $p$ -value $\le \alpha$ , reject $H_0$ ("If $p$ is low, $H_0$ must go")?
Does independent events imply mutually exclusive events? NO! If $P(A) > 0, P(B) > 0$ , independent events can never be mutually exclusive.

Previous Topic: ◇CSMATH1
Next Topic: ◇CSMODEL
Prerequisites: ◇Probability and Statistics, Bayes, Distributions, Hypothesis Testing
Cross-Curricular Connections: ◇CSINTSY

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