Suppose X1;X2;...;X5 is a random sample from a n(0; variance) distribution. define

U = X1+X2+X3+X4;
V = (X2)^2+(X3)^2+(X4)^2+(X5)^2
and W = U/sqrtV.

(a) Name the distribution of U/4 and V/(variance) and give the values of their parameters.
(b) (i) Compute k such that kW has a t-distribution.
(ii) Give the number of degrees of freedom of this t-distribution.
(c) Compute E(V).

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