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VCE 12 Methods 2023

8.06 Binomial distribution

Interactive practice questions

Which of the following statements is true?

In a binomial experiment, there are $n$n repeated, dependent trials.

A

In a binomial experiment, there are $n$n repeated, independent trials.

B

In a binomial experiment, there are exactly two trials.

C

In a binomial experiment, there is exactly one trial.

D
Easy
< 1min

Which of the following statements is true?

Easy
< 1min

Does rolling a six-sided die $20$20 times and counting the number of times the die lands on $1$1 describe a binomial random variable?

Easy
< 1min

Can the sum of the outcomes of rolling a six-sided die $10$10 times describe a binomial random variable?

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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