6. [Optional] The expectation and variance of a random variable are dened. respectively as E(X) = #X = Z xp(x) and V(X) : E (X E(X))2 . I Let a and b be constants. Use the definitions to Show that (a) E(aX+b) = aE(X)+b (b) 1/00 = 150(2) 415(an (c) V(aX + b) = (fl/(X) 7. [Compulsory] The following summary quantities for x, the shear force (kg) and y _, the percent ber dry weight ofasparagus calculated from a representative sample data: n :18, 2x]. =1950, 2x3 =251.970, 2,12,. 247.92, 2y? 2130,6074. in,1,;=5530.92 Calculate the value of the sample correlation coefficient