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VCE 12 Methods 2023

8.04 Applications of general discrete random variables

Interactive practice questions

An investment scheme advertises the following percentage returns after $2$2 years based on historical probabilities.

Percentage return ($x$x) $10%$10% $15%$15% $25%$25%
$P\left(X=x\right)$P(X=x) $0.7$0.7 $0.15$0.15 $0.15$0.15
a

Calculated the expected percentage return on investment.

Give your answer as a percentage.

b

If someone invested $\$50000$$50000, how much could they expect their investment to be worth after $2$2 years?

Easy
2min

A salesperson is starting work in a new region and analyses the probability of how many sales he is likely to make in the next month.

Easy
4min

At a car park in the city, all day parking is charged on the following basis below.

Medium
5min

Two dice are rolled and the absolute value of the differences between the numbers appearing uppermost are recorded.

Medium
7min
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Outcomes

U34.AoS4.2

discrete random variables: - specification of probability distributions for discrete random variables using graphs, tables and probability mass functions - calculation and interpretation of mean, 𝜇, variance, 𝜎^2, and standard deviation of a discrete random variable and their use - Bernoulli trials and the binomial distribution, Bi(𝑛, 𝑝), as an example of a probability distribution for a discrete random variable - effect of variation in the value(s) of defining parameters on the graph of a given probability mass function for a discrete random variable - calculation of probabilities for specific values of a random variable and intervals defined in terms of a random variable, including conditional probability

U34.AoS4.10

calculate and interpret the probabilities of various events associated with a given probability distribution, by hand in cases where simple arithmetic computations can be carried out

U34.AoS4.11

apply probability distributions to modelling and solving related problems

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