Prior content: None
Previous Section: Correlation
Next Section: Combinations of Random Variables*
Contents
- Whole Topic Notes
- 3A Continuous Random Variables
- 3B The Cumulative Distribution Function
- 3C Mean and Variance of a Continuous Distribution
- 3D Mode, Median, Percentiles and Skewness
- 3E The Continuous Uniform Distribution
- 3F Modelling with the Continuous Uniform Distribution
- Whole Topic Summary Resources (Including Past Paper Questions)
Whole Topic Notes
Full Notes to Accompany Examples
Dr Frost
- Dr Frost Further Statistics 2 Continuous Distributions Section
- Dr Frost Further Statistics 2 Continuous Distributions Slides
3A Continuous Random Variables
Textbook resources
FMSP Video Courtesy of MEI
Dr Frost resources
No Live Lesson Video Yet
Download Slides
Key Skills
Note all numbers are subject to change and will be updated once all key skills have been finished by Dr Frost
- 862a: Sketch a probability density function.
- 862c: Determine a constant in a probability density function with a single interval.
- 862d: Determine a constant in a probability density function with multiple intervals.
- 862e: Determine the probability mass for a range P(a < X < b) across a single interval.
- 862f: Determine the probability mass for a range P(a < X < b) across multiple intervals.
- 862: Exam Practice: Probability density functions and areas under their graphs
Worksheets
- Mathshelper (Jon Stone)
3B The Cumulative Distribution Function
Textbook resources
No Video Yet
Dr Frost resources
No Live Lesson Video Yet
Download Slides
Key Skills
Note all numbers are subject to change and will be updated once all key skills have been finished by Dr Frost
- 863a: Determine F(x) for a probability density function with a single interval.
- 863b: Determine F(x) for a probability density function with multiple intervals.
- 863c: Determine a probability P(X > k) or P(X < k) using F(k)
- 863d: Determine a probability P(a < X < b) using F(k)
- 863e: Determine the probability density function f(x) from F(x)
- 863: Exam Practice: Cumulative distribution functions for continuous random variables
3C Mean and Variance of a Continuous Distribution
Textbook resources
No Video Yet
Dr Frost resources
No Live Lesson Video Yet
Download Slides
Key Skills
Note all numbers are subject to change and will be updated once all key skills have been finished by Dr Frost
- 864a: State E(X) for a symmetric probability density function.
- 864b: Determine E(X) using a probability density function with a single interval.
- 864d: Determine Var(X) using a probability density function with a single interval.
- 864e: Determine E(aX + b) using a probability density function.
- 864f: Determine Var(aX + b) using a probability density function.
- 864g: Determine E(X) using a probability density function with multiple intervals.
- 864h: Determine Var(X) using a probability density function with multiple intervals.
- 864i: Determine E(X²) using a probability density function.
- 864j: Determine E(g(X)) for a continuous random variable X where g(X) is an arbitrary function.
- 864: Exam Practice: Mean and variance of continuous random variables
3D Mode, Median, Percentiles and Skewness
Textbook resources
No Video Yet
Dr Frost resources
No Live Lesson Video Yet
Download Slides
Key Skills
Note all numbers are subject to change and will be updated once all key skills have been finished by Dr Frost
- 865a: Determine the mode of a continuous random variable.
- 865b: Determine the median of a continuous random variable using the cumulative density function.
- 865c: Determine the median of a continuous random variable using the probability density function.
- 865d: Determine the lower or upper quartile of a continuous random variable using the cumulative density function.
- 865f: Determine the interquartile range of a continuous random variable using the cumulative density function.
- 865g: Determine a percentile of a continuous random variable using the cumulative density function.
- 865h: Determine with a continuous random variable is positively or negative skewed from a sketch of its probability density function.
- 865: Exam Practice: Mode, median and percentiles of continuous random variables
3E The Continuous Uniform Distribution
Textbook resources
No Video Yet
Dr Frost resources
No Live Lesson Video Yet
Download Slides
Key Skills
Note all numbers are subject to change and will be updated once all key skills have been finished by Dr Frost
- 866b: State the probability density function of a rectangular distribution.
- 866c: Determine the probability of a range for a rectangular distribution, not in context.
- 866e: Calculate a conditional probability using a rectangular distribution.
- 866f: Determine E(X) for a rectangular distribution.
- 866g: Determine Var(X) for a rectangular distribution.
- 866h: Determine Var(aX + b) for a rectangular distribution.
- 866i: Determine E(X²) for a rectangular distribution.
- 866j: Determine the bounds of a rectangular distribution given E(X) and Var(X).
- 866l: State the cumulative density function for a rectangular distribution.
- 866: Exam Practice: Continuous uniform (rectangular) distribution
3F Modelling with the Continuous Uniform Distribution
Textbook resources
No Video Yet
Dr Frost resources
No Live Lesson Video Yet
Download Slides
Key Skills
Note all numbers are subject to change and will be updated once all key skills have been finished by Dr Frost
- 866a: Choose from a normal, binomial, Poisson, geometric or continuous uniform distribution to best model a given context.
- 866d: Determine the probability of a range for a rectangular distribution, in context.
- 866i: Determine E(X²) for a rectangular distribution.
- 866: Exam Practice: Continuous uniform (rectangular) distribution