Statistics 2

Worked examples (5)

• 1Probabilities from a continuous uniform (4 marks, S2)
• 2Mean and variance of a uniform (4 marks, S2)
• 3CDF, median, and inverse problem (6 marks, S2)
• 4Modelling waiting time as uniform (5 marks, S2)
• 5Derive mean and variance from definition (6 marks, S2)

Worked examples (5)

• 1Single-point probability $P(X = r)$ (3 marks, S2)
• 2Cumulative probability $P(X \\le c)$ (4 marks, S2)
• 3Mean and variance, with $P(X \\ge 5)$ (5 marks, S2)
• 4Inverse cumulative — find smallest $c$ (5 marks, S2)
• 5Modelling validity — when is binomial appropriate? (5 marks, S2)

Worked examples (5)

• 1Single-point Poisson probability (4 marks, S2)
• 2Cumulative Poisson and upper tail (5 marks, S2)
• 3Time scaling — different intervals (5 marks, S2)
• 4Sum of independent Poissons (5 marks, S2)
• 5Poisson modelling validity (5 marks, S2)

Worked examples (5)

• 1Binomial $\\to$ Poisson approximation (5 marks, S2)
• 2Binomial $\\to$ Normal with continuity correction (6 marks, S2)
• 3Poisson $\\to$ Normal with continuity correction (6 marks, S2)
• 4Continuity corrections for $u003c, \\le, u003e, \\ge, =$ (5 marks, S2)
• 5Justifying the choice of approximation (4 marks, S2)

Worked examples (5)

• 1Verify a PDF and compute probability (5 marks, S2)
• 2Mean and variance of a continuous RV (6 marks, S2)
• 3Find and use the CDF (6 marks, S2)
• 4Find the median (4 marks, S2)
• 5Find the mode (3 marks, S2)

Worked examples (5)

• 1Population, sample, statistic (4 marks, S2)
• 2Simple random sample procedure (5 marks, S2)
• 3Sampling distribution of $\\bar X$ (6 marks, S2)
• 4Effect of sample size on SE (5 marks, S2)
• 5CLT for non-normal parent (5 marks, S2)

Worked examples (5)

• 1One-tail binomial hypothesis test (7 marks, S2)
• 2Critical region for a binomial test (7 marks, S2)
• 3Poisson hypothesis test (7 marks, S2)
• 4Hypothesis test using normal approximation (7 marks, S2)
• 5Type 1 and Type 2 errors — informal (4 marks, S2)