Q2: Show that Y and X have the same distribution. Hint: compute the cdf of Y, FY(x)=P(Yx) Let us now see how we can use the previous property and the uniform random variable U to sample a different from a different distribution with a known density. In the following, we let C denote a random variable with a Cauchy distribution. The probability density function f of a random variable with Cauchy distribution is given by f(x)=(1+x2)1