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Homework answers / question archive / 3) Rotational invariance and correlation: Y ~ unif(Bn) and U ~ unif(Sn-1) a) With Xi = U2i, determine EX1, s(X1) and r(X1, X2)

3) Rotational invariance and correlation: Y ~ unif(Bn) and U ~ unif(Sn-1) a) With Xi = U2i, determine EX1, s(X1) and r(X1, X2)

Math

3) Rotational invariance and correlation: Y ~ unif(Bn) and U ~ unif(Sn-1)

a) With Xi = U2i, determine EX1, s(X1) and r(X1, X2).

b) With Vi = Y2i, determine EV1, s(V1) and r(V1, V2).

5) Order statistics with the standard exponential: Z1,……., Zn IID Z ~ exp(1), n Î N

a) With Z0 = 0, determine the joint distribution of the coverage, Z(i) – Z(i-1), I = 1, …., n.

b) using the result in a), or otherwise, obtain EZ(i) and s(Z(i)) for every 1 £ i £ n as well as the correlation coefficients r(Z(i), Z(j)) for 1 £ i < j £ n.

 

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