CIE AS & A Level Maths : Probability & Statistics 2 Paper 6 -Exam Style Question New Syllabus - 2027-2028
CIE A Level Maths : Probability & Statistics 2 Paper 6 Exam Questions – New Syllabus 2027-2028
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Probability & Statistics 2 – Paper 6
Topic-wise Exam Style Questions with syllabus-based subtopics for Paper \(6\)
The Poisson Distribution
- Calculating probabilities for \(X\sim \operatorname{Po}(\mu)\)
- Mean and variance of a Poisson distribution
- Poisson distribution as a model for random events
- Poisson approximation to the binomial distribution
- Conditions such as large \(n\), small \(p\), and approximately \(np<5\)
- Normal approximation to the Poisson distribution with continuity correction
Linear Combinations of Random Variables
- Using \(E(aX+b)=aE(X)+b\)
- Using \(\operatorname{Var}(aX+b)=a^2\operatorname{Var}(X)\)
- Finding \(E(aX+bY)\)
- Finding \(\operatorname{Var}(aX+bY)\) for independent \(X\) and \(Y\)
- Linear combinations of normal random variables
- Sums of independent Poisson random variables
Continuous Random Variables
- Understanding continuous random variables
- Probability density functions \(f(x)\)
- Using \(\int f(x)\,dx=1\) over the valid range
- Finding probabilities using areas under a density curve
- Finding the median and percentiles using areas
- Calculating the mean and variance of a distribution
Sampling and Estimation
- Distinction between a sample and a population
- Importance of randomness in sampling
- Recognising unsuitable sampling methods
- Sample mean as a random variable
- Using the Central Limit Theorem
- Unbiased estimates of population mean and variance
- Confidence intervals for a population mean
- Approximate confidence intervals for a population proportion
Hypothesis Tests
- Nature of a hypothesis test
- Null and alternative hypotheses
- One-tailed and two-tailed tests
- Significance level, critical region and test statistic
- Hypothesis tests using binomial and Poisson distributions
- Tests for a population mean using normal distribution
- Type I and Type II errors
- Calculating error probabilities in specific situations
Probability & Statistics \(2\) – Paper \(6\) Full Access
Get complete access to CIE AS & A Level Mathematics \(9709\) Probability & Statistics \(2\) Paper \(6\) topic-wise questions with detailed solutions.
AS & A Level Maths Paper \(6\) – Full Access