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Q2 Let X ,X2, ..., X, be a random sample consisting of independent random variables with mean u and variance o? Consider the sample mean: In your answer you may denote u by mu, o2 by sigma2 and X by Xbar. (i) Write down the expected value of X. n (ii) Derive the variance of X. [2] Comment on the variance of variable X as compared to the variance of Xi. [1] An actuary is interested in exploring the difference in the size of claim losses from two insurance portfolios, and can take samples of claims from these portfolios. (iv) Explain how the answer to part (iii) can affect the precision of the actuary's comparison [2] [Total 6] Q2 Let X ,X2, ..., X, be a random sample consisting of independent random variables with mean u and variance o? Consider the sample mean: In your answer you may denote u by mu, o2 by sigma2 and X by Xbar. (i) Write down the expected value of X. n (ii) Derive the variance of X. [2] Comment on the variance of variable X as compared to the variance of Xi. [1] An actuary is interested in exploring the difference in the size of claim losses from two insurance portfolios, and can take samples of claims from these portfolios. (iv) Explain how the answer to part (iii) can affect the precision of the actuary's comparison [2] [Total 6]

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