Question 1(a)
[Maximum number: 1]
Two fair coins are thrown at the same time repeatedly until a pair of heads is obtained. The number of throws taken is denoted by the random variable X.
State the value of E(X).
CAIE A-Level Mathematics 5.4.3 Expectation and Variance
Practise using standard expectation and variance formulae for binomial variables and the expected waiting time for geometric variables, with parameters read from context.
How this is tested
- for X distributed B(n, p), calculate E(X) = np and Var(X) = np(1 − p) from its parameters
- for X distributed Geo(p), calculate the expected trial of first success as E(X) = 1/p
- identify n and p from the experiment before substituting and interpret the resulting mean