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VCE 12 Methods 2023

8.05 Bernoulli distribution

Interactive practice questions

Which of the following describes a Bernoulli random variable?

Select all that apply.

A dice is rolled. $X=$X=the number appearing uppermost on the dice

A

Two coins are tossed. $X=$X=the number of heads tossed

B

Two coins are tossed. $X=1$X=1 if at least one head shows, $X=0$X=0 if there are no heads showing.

C

A dice is rolled. $X=1$X=1 if an even number shows uppermost, $X=0$X=0 if an odd number shows uppermost.

D
Easy
1min

Which of the following describes a Bernoulli random variable?

Easy
< 1min

A family with three children is chosen at random from the Australian census and whether the family has three girls is observed.

Easy
4min

A dice is rolled once in an experiment and the focus is on whether a $4$4 appears uppermost on the dice.

Easy
1min
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Outcomes

U34.AoS4.5

the concepts of a random variable (discrete and continuous), Bernoulli trials and probability distributions, the parameters used to define a distribution and properties of probability distributions and their graphs

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.AoS4.6

the conditions under which a Bernoulli trial or a probability distribution may be selected to suitably model various situations

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