Recent content by thisguy12

Okay so using the transformation method, I found the density functions for U = Y^2_1 and W = Y^2_2. h(Y) = U = Y^2_1 h^{-1}(U) = Y_1 = \sqrt{U} \frac{d[h^{-1}(u)]}{du} = \frac{1}{2\sqrt{u}} f_U(u) = f_{Y_1}(\sqrt{u}) \frac{1}{2\sqrt{u}} = 1(\frac{1}{2\sqrt{u}})=\frac{1}{2\sqrt{u}}...

If you were to pick two random numbers on the interval [0,1], what is the probability that the sum of their squares is less than 1? That is, if you let Y_1 ~ U(0,1) and Y_2 ~ U(0,1), find P(Y_1^2 + Y^2_2 \leq 1). There is also a hint: the substitution u = 1 - y_1 may be helpful - look for a beta...

Let W_1 and W_2 be independent Chi-Squared distributed random variables with v_1 and v_2 degrees of freedom, respectively. Then F = (W_1/v_1)/(W_2/v_2) = (v_2/v_1)(W_1/W_2) is said to have an F-distribution with v_1 numerator degrees of freedom and v_2 denominator degrees of freedom. I want...