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9. Continuous random variables
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VCE 12 Methods 2023

9.01 Continuous random variables

Lesson
Worksheet
Practice

Interactive practice questions

At the beginning of the year, a teacher seats his students alphabetically to learn their names quickly.

a

Can we use a probability distribution to model where a particular child will sit in the class?

No

A

Yes, a discrete probability distribution

B

Yes, a continuous probability distribution

C
b

Which of the following explains why a probability distribution doesn’t exist for this situation?

The outcomes are not random.

A

The outcomes are not variable.

B
Easy
< 1min

A manager randomly selects four people from his Sales team and two people from his Development team to attend a leadership conference.

Easy
< 1min

A manager randomly selects three of his staff to attend a leadership conference. He randomly selects people from his Sales team and his Development team.

Medium
< 1min

The traffic signal at a particular pedestrian crossing remains red for $3$3 minutes.

Frank arrives at the pedestrian crossing to find that the light is currently red.

Medium
< 1min
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Outcomes

U34.AoS4.9

analyse a probability mass function or probability density function and the shape of its graph in terms of the defining parameters for the probability distribution and the mean and variance of the probability distribution

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, πœ‡, 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(πœ‡, 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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