Let F1 and F2 be CDFs, 0 < p < 1, and F(x)= pF1(x)+(1p)F2(x) for all x. The distribution dened by F is called a mixture of the distributions dened by F1 and F2. Consider creating an r.v. in the following way. Flip a coin with probability p of Heads. If the coin lands Heads, generate an r.v. according to F1; if the coin lands Tails, generate an r.v. according to F2. Show that the r.v. obtained in this way has CDF F.