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AustraliaVIC
VCE 12 Methods 2023

8.03 Centre and spread of discrete random variables

Interactive practice questions

Consider the table.

$x$x $0$0 $1$1 $2$2 $3$3 $4$4
$P$P$($($X=x$X=x$)$) $0.1$0.1 $0.45$0.45 $0.15$0.15 $0.05$0.05 $0.25$0.25
a

Does the table represent a discrete probability distribution?

Yes

A

No

B
b

What is the most likely outcome for the random variable $X$X?

c

Calculate $E\left(X\right)$E(X).

Easy
2min

Consider the probability distribution table shown for the random variable $X$X.

Easy
1min

Consider the probability distribution shown.

Easy
1min

Consider the probability distribution table shown for the random variable $X$X.

Easy
1min
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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

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