STATISTICAL DISTRIBUTIONS
Applied Year 1, Chapter 6
Probability distributions
โขCapital letters are used for
the whole distribution of
outcomes (called a random
variable): ๐, ๐
โขLower case letters are used
for a particular value of the
random variable: ๐ฅ, ๐ฆ
โขDistributions can be
presented in tables
โขA discrete uniform
distribution is one where
the probabilities are all
uniform (i.e. equal)
โขAs usual, ฯ๐ = 1
Mr Bicen selects three letters at random, one at a time without replacement, from the word โMATHEMATICSโ.
The discrete random variable ๐ represent the number of times he selects the letter โMโ.
Complete the probability distribution for ๐
๐ฅ 0 1 2
๐(๐ = ๐ฅ) 3
55
In a video game, a player can either win 0, 1, 2 or 3 coins for a particular action.
The random variable ๐ represents the number of coins won and has the following probability distribution,
where ๐ and ๐ are constants.
a) Given that the probability of winning at least 2 coins is two thirds the probability of winning 0 coins, find
the values of ๐ and ๐.
b) Given that each outcome is independent of previous outcomes, calculate the probability that a total of
exactly 2 coins is won when completing the action twice.
๐ฆ 0 1 2 3
๐(๐ = ๐ฆ) 2๐ ๐ ๐ 0.05
