This question is about mean vectors, variance matrix and covariance.

1. Sam Bloggs has recorded the rainfall (in centimetres) for a week as r1=0, r2=1, r3=3, 731:4, r5=2, r5=2 and r7=0, where 7'7; is the recorded rainfall on day i. The data are put into six vectors, where each vector's components are two consecutive days' rainfalls, with the rst component as the later of the two days, viz. r- . i=( 1+1) for z=1,...,6 Ti (a) Calculate the mean vector and variance matrix for the six data points g1, . . . ,g5. (b) What is the covariance between the rst and second components of the ii? (0) What does the sign of the covariance you identied in part (b) tell you about rainfall on consecutive days? ((1) If the covariance had the opposite Sign what would that tell you about rainfall on consecutive days