Determine if each function in the following exercise is atransformation and collineation. a) f(x,y) = (3x - 5y, x + 4y) b) g(x,y) = (y5, 4x - x3) Determine if each function in the following exercise is atransformation and collineation. a) f(x,y) = (3x - 5y, x + 4y) b) g(x,y) = (y5, 4x - x3) Solution all automorphisms are collineations. clearly, a) f(x,y) = (3x - 5y, x + 4y) is a bijective lineartransformation on R2 . so, it is a collineation. (b) g(x,y) = (y5, 4x - x3) is also acollineation while the function projects the collinear points onthe the collinear points by showing g (x1,y1) = g(x2,y2)==> ( x1,y1) = (x2,y2)..

1. Determine if the each of the following is a probability distribution or not. Explain your
reasoning. (5 points each)
11.
x 0 1 2 3 4
P(x) 0.1 0.2 0.1 0.5 0.2
12.
x 1 2 3 4
P(x) ¼ 0 ½ ¼
Solution
11. no sum of probabilities does not add up to 1. 12 yes, sum of probabilities adds
up to 1 and all are between 0 and 1.