Problem 1 Consider the following experiment: we roll a fair die. If a six comes up we flip a fair coin unitl the first "heads", otherwise we roll the die until the first "six". Let the random variable X be the the number of flips or rolls until the experiment is finished, not counting the original roll. Find the pmf of X.

Problem 2 Let the discrete rv X have pmf f(k)=c/(k(k+1)), k=1,2,3,... Find c.

Problem 3 Let f(x)=c/√(2x+1), 0<x<1 be a density. Find c.

Problem 4 Let f(x,y)=c, 0<x<y²<1 be a joint density. Find c.