CAIE A-Level Mathematics 6.4.3 Sample mean

Practise treating a sample mean as a random variable and applying its expectation and variance when samples are taken from a population.

[Maximum number: 1]

A random sample of 5 values of a variable X is given below.

\begin{array}{lllll} 2 & 3 & 3 & 5 & a \end{array}

Find an expression, in terms of a, for the mean of these values.

It is given that an unbiased estimate of the population variance of X, using these values, is 4. It is also given that a is positive.

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6.4.3—Sample mean question 1