Problem on Independent Trials: (20 Points) Consider a sequence of indepen dent trials {1}}:1 , where trial T,- yields a success (S) with probability p or a failure (F) with probability 1 p. 1. (5 points) Let M be the number of 'S' in trial T1. Please provide the sample space of M (Le, SM) and the probability, P[M = m], where m 6 SM. 2. ( 5 points) Let Y be the number of 'S's in the rst 71 trials, where n 2 1. Please provide the sample space of Y (i.e., Sy ) and the probability, P[Y = y], where y E Sy. 3. (5 points) Let X be the number of trials needed to get the rst success. Please provide the sample space of X (Le.3 S'X ) and the probability, P[X = m], where SE E 8);. 4. (5 points) Let Z be the number of trials needed to get the rst k 2 1 successes. Please provide the sample space of Z (i.e., SZ ) and the probability, P[Z = z], where z E 82