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SingaporeMaths

Probability and Statistics

10 dot points across 10 inquiry questions. Click any dot point for a focused answer with worked past exam questions where available.

When do the binomial and Poisson distributions apply, and how do we compute their probabilities?

Model situations with the binomial and Poisson distributions, state the conditions for each, and compute probabilities, means and variances
A focused answer to the H2 Mathematics outcome on the binomial and Poisson distributions. The conditions for each model, their probability functions, means and variances, and choosing the right model.
10 min answer →

How does conditioning on information change a probability, and what does independence mean?

Calculate conditional probabilities, test for independence, and apply the conditional probability formula and the law of total probability
A focused answer to the H2 Mathematics outcome on conditional probability. The conditional formula, testing independence, the law of total probability, and reasoning with given information.
9 min answer →

How do we measure the strength of a linear relationship and fit a line for prediction?

Compute and interpret the product moment correlation coefficient, find the least squares regression line, and use it for prediction within the data range
A focused answer to the H2 Mathematics outcome on correlation and regression. The product moment correlation coefficient, the least squares regression line, choosing which line to use, and the limits of prediction.
9 min answer →

How do we describe a discrete random variable and compute its expectation and variance?

Construct probability distributions for discrete random variables and compute the expectation and variance, including for functions of the variable
A focused answer to the H2 Mathematics outcome on discrete random variables. Building a probability distribution, the expectation and variance formulae, and the effect of linear transformations on mean and variance.
9 min answer →

How do we test a claim about a population mean using sample evidence?

Carry out a hypothesis test for a population mean, stating hypotheses, computing a test statistic or p-value, and interpreting the conclusion in context
A focused answer to the H2 Mathematics outcome on hypothesis testing. Setting up null and alternative hypotheses, one- and two-tailed tests, the test statistic and p-value, the significance level, and interpreting the conclusion.
10 min answer →

When can the binomial or Poisson be approximated by the normal or Poisson, and how is the continuity correction applied?

Approximate the binomial by the Poisson or the normal, and the Poisson by the normal, under stated conditions, applying a continuity correction where appropriate
A focused answer to the H2 Mathematics outcome on distribution approximations. The conditions for the Poisson and normal approximations to the binomial and the normal approximation to the Poisson, and the continuity correction.
10 min answer →

How do we compute probabilities for a normally distributed variable using standardisation?

Model continuous data with the normal distribution, standardise to the Z-distribution to find probabilities, and find values from given probabilities
A focused answer to the H2 Mathematics outcome on the normal distribution. The bell curve and its parameters, standardising to Z, finding probabilities and inverse problems, and combining normal variables.
10 min answer →

How do we count arrangements and selections, and when does order matter?

Use the addition and multiplication principles, permutations and combinations to count arrangements and selections, including cases with restrictions
A focused answer to the H2 Mathematics outcome on counting. The addition and multiplication principles, permutations where order matters, combinations where it does not, and handling restrictions and identical objects.
9 min answer →

How do we calculate probabilities of combined events using the basic rules?

Use the probability rules for the complement, union and intersection of events, and apply Venn diagrams and tree diagrams to combined events
A focused answer to the H2 Mathematics outcome on probability rules. The complement, addition and multiplication rules, mutually exclusive events, and using Venn and tree diagrams for combined events.
9 min answer →

How does the distribution of a sample mean behave, and what does the Central Limit Theorem guarantee?

Describe the distribution of the sample mean, use the Central Limit Theorem, and find unbiased estimates of the population mean and variance from a sample
A focused answer to the H2 Mathematics outcome on sampling. The distribution of the sample mean, the Central Limit Theorem, the standard error, and unbiased estimators of the population mean and variance.
9 min answer →