CAIE A-Level Mathematics AS 5.4.3 Expectation and Variance Questions

Practise calculating and interpreting the expected value of a discrete random variable.

Exam points

calculate expected values from probability distributions
use expected value to find unknown distribution parameters
interpret the mean of a discrete random variable in context

[Maximum number: 2]

An ordinary fair die is thrown repeatedly until a 1 or a 6 is obtained.

On another occasion, this die is thrown 3 times. The random variable X is the number of times that a 1 or a 6 is obtained.

Find E(X).

$E(X)=0\left(\frac8{27}\right)+1\left(\frac{12}{27}\right)+2\left(\frac6{27}\right)+3\left(\frac1{27}\right).$ $E(X)=\frac{12}{27}+\frac{12}{27}+\frac3{27}=1.$

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CAIE A-Level Mathematics AS 5.4.3 Expectation and Variance Questions question 1