Problem on Independent Trials: (20 Points) Consider a. sequence of indepen- dent trials {1",}:1 , where trial T,- yields a success [8) with probability p or a failure (F) with 1:1rolraabilit}r 1 p, 1. {5 points) Let M be the number of 'S' in trial T1, Please provide the sample space of M {i.e., SM) and the probability, PM! 2 m], where m 6 SM. 2. {5 points} Let Y be the number of 'S's in the rst 11 trials, where n :3 1' Please provide the sample space of Y {i.e., Sy } and the probability, P[Y = y], where y E 3y. 3. {5 points) Let X be the number of trials needed to get the rst success. Please provide the sample space of X [i.e., Sx ] and the probability, P[X = :3], where I E 31*. 4. (5 points} Let Z be the number of trials needed to get the rst 1:: 3: 1 successes. Please provide the sample space of Z (Le, SE } and the probability, PIZ = z], where z E 3