1. (a) The discrete random variables X and Y represent the number of errors made in obtaining the X and Y coordinates respectively, of a survey point. The joint distribution function of X and Y is given by: F(x,y)={(k(2x+y⁄3), x=0,1,2 and y=1,2,3 0, elsewhere} ,where k is a constant.
(i) Determine the value of the constant k. [4 marks]
(ii) Find P(X=1,Y=1) and P(X>0,Y>0). [3 & 3 marks]
(b) For another survey point, the Y coordinates is known, and thus only the X coordinate must be obtained. X represents the number of errors made in obtaining the X coordinate of the survey point. The probability function of X is given by: p(x)=24/(x!(4-x)!) * (0.6)^x (0.4)^(4-x) for x=0,1,2,3,4
(i) Evaluate and plot F(x)=P(X≤x) for -1
(ii) Evaluate P(1
