# Probability density functions

Video unpacking question 7 from the NESA sample examination paper which looks at probability density functions.

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Watch the video Probability density functions unpacking a question from the sample exam (1:27).

Answering the question on probability density from the sample exam

### Transcript of mathematics advanced probability density functions

#### Meagan Rodda

This is the HSC hub Mathematics curriculum support from the New South Wales Department of Education. My name is Meagan Rodda. This question is from the NESA sample exam and incorporates material from the statistical analysis strand in the mathematics advanced course. This question looks at a probability density function.

We acknowledge that there may be different approaches, methods or techniques to answering this question, and we encourage you to discuss and share these ideas with each other. Please take a moment to read the question before we continue.

A continuous probability distribution is represented by a function called a probability density function, where X is the random variable. The mode is the maximum point of the probability density function. In this probability density function, the highest point is 0.8 comma 0.6, so we can automatically rule out options A and D. The highest point occurs when X equals 0.8, so therefore the mode is 0.8 and the correct answer is C.

This is the HSC hub for the New South Wales Department of Education.

[End Transcript]

## Syllabus

Mathematics Advanced Stage 6 Syllabus © NSW Education Standards Authority (NESA) for and on behalf of the Crown in right of the State of New South Wales, 2017

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