Topics
9. Continuous random variables
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AustraliaVIC
VCE 12 Methods 2023

9.03 Centre and spread

Lesson
Worksheet
Practice

Interactive practice questions

Consider the following.

a

Select the option which shows two distributions with the same expectation.

A

B

C

D
b

Consider the graphs of the two distributions below.

Which of the following scenarios could be modelled by these two distributions?

The length of two species of fish A and B which have the same average length, but where the length in of species B varies more than in the other.

A

The battery life of two different brands of phones A and B, where phone A has a longer average battery life but the variation in battery life among the two phones is the same.

B
Easy
< 1min

Consider the following.

Easy
< 1min

Consider the probability density function $p\left(x\right)=\frac{1}{40}$p(x)=140​ when $10\le x\le50$10≤x≤50.

Easy
1min

Consider the probability density function $p\left(x\right)=\frac{3}{160}\left(x^2+4x\right)$p(x)=3160​(x2+4x) when $0\le x\le4$0≤x≤4.

Medium
2min
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Outcomes

U34.AoS4.3

continuous random variables: - construction of probability density functions from non-negative functions of a real variable - specification of probability distributions for continuous random variables using probability density functions - calculation and interpretation of mean, 𝜇, variance, 𝜎^2, and standard deviation of a continuous random variable and their use - standard normal distribution, N(0, 1), and transformed normal distributions, N(𝜇, 𝜎^2), as examples of a probability distribution for a continuous random variable - effect of variation in the value(s) of defining parameters on the graph of a given probability density function for a continuous random variable - calculation of probabilities for intervals defined in terms of a random variable, including conditional probability (the cumulative distribution function may be used but is not required)

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