Decide whether the linear transformations in Exercises 16 through 20 are invertible. Find the inverse transformation if it exists. Do the computations with paper and pencil. Show all your work.

11/2/15 1.) Random values take their values from an interval of real numbers, possibly all real numbers 2.) Have a probability density function (pdf) 3.) Positive probabilities (correspond to) areas under a probability density function 4.) The entire area under a pdf is 1 x is uniform of [0,10]. More general example Uniform on [a,b] Atriangle distribution on [0,1] We need: 1.) Normal distributions 2.) “Student-t” (or just “t”) 3.) “Chi-square” (x^2) • on [0, inﬁnity] 1.) Normal Distributions: completely determined by a mean and a standard deviation. Ex.) x= height of adult human male Mean = 69 in St. Dev = 3 in y = weight of adult human male Mean = 170 St. Dev = 30 *The standard normally distributed random variable is called z and h