S1 Statistics Revision - Chapter 8 Notes

Chapter 8 - Discrete random variables

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AS Statistics Revision
Statistics 1 ­ Chapter 8
Discrete Random Variables
Key points to remember
Random variable X = a variable that represents the values
obtained when we take a measurement from an experiment in
the real world.
Discrete random variable = a variable that changes by steps,
takes only specified values in any given interval.
Probability function = a function that describes how the
probabilities are assigned
Probability distribution = the set of all the values of a random
variable together with their associated probabilities. For
X 1 2 3 4 5 6
P(X=x) 1/6 1/6 1/6 1/6 1/6 1/6
is the probability distribution which describes the values, x,
when a die is thrown and the associated probabilities. Note
P(X=x) is sometimes written as p(x).
Sum of all probabilities = p(x) = 1
The expected value of X = E(X) = xP(X=x) = xp(x)
The expected value for X² = E(X²) = x²P(X=x)
The Variance of X = Var(X) = E(X²) ­ ((E(X))²
Expectation of a linear function of X = E(aX + b) aE(X) + b
Variance of a linear function = Var(aX + b) a² Var(X)



Thank you for all of these :)

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