# Statistics

posted by
**ruth**
.

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).