Sign In Sign Up Ask an AI advisor
yasmin7740
yasmin7740
06.04.2021 • 
Mathematics

g Let Θ ∼ Uniform[0, 2π]. Let X = cos Θ, Y = sin Θ. (a) Show that X and Y are uncorrelated random variables (b) Show that X and Y are not independent random variables by showing that X2 and Y 2 are not uncorrelated random variables. (c) Show that X and Y are not independent random variables by showing that {− √ 1 2 < X < √ 1 2 }, {− √ 1 2 < Y < √ 1 2 } are not independent events. Remark: (b) and (c) are indirect ways of showing that X and Y are not independent.

Solved
Show answers

Ask an AI advisor a question

I want advice