Please help with 1-4

Problem on Independent Trials: (20 Points) Consider a sequence of indepen dent trials {To} , 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 71. Please provide the sample space of M (i.e., SM) and the probability, P[M = m], where m E SM. 2. (5 points) Let Y be the number of 'S's in the first n trials, where n > 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 first success. Please provide the sample space of X (i.e., Sx ) and the probability, P[X = x], where TE Sx . 4. (5 points) Let Z be the number of trials needed to get the first k 2 1 successes. Please provide the sample space of Z (i.e., Sz ) and the probability, P[Z = =], where z E Sz

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