1. A fair coin is tossed 4 times. What\'s one of the simple events from this experiment (where H denotes heads on a coin and T tails on a coin)? A. H, T B. HTHT C. TH D. None of the above 2. Same setup as in Q#1. Let X denote the number of heads observed. Whats the range of X? A. The sample space of the experiment B. The sample as the pmf of X C. {0,1,2,3,4 } D. {0, 1} 3. Same setup as in Q#2. What\'s the value of X when you observe 3 tails? A. 0 B.1 C.2 D.3 4. Same setup as in Q#2. What\'s the value of f(1) for X? A. 1/16 B. 1/4 C. 1/2 D. 1 5. What does the ex ante mean as a propertt of a statistical measure? A. That the stat measure is given before observation are taken B. That the stat measure is unknown in its true value C. That the stat measure is a continuous random variable D. Taht the stat measure has positive pmf values Solution Hey, Answers and explanations are as follows: 1) Possible simple events for this experiment are HHHH,HHHT,HHTH,.....TTTH,TTTT Among the options, option (B) = HTHT is a possible simple event. HTHT = 4 coin tosses wherein first toss resulted in a Heads second toss resulted in a Tails third toss resulted in a Heads fourth toss resulted in a Tails Option (B) 2) Out of 4 coin tosses, these are the possiblities: [0 heads, 4 tails] , [1 head, 3 tails], [2 heads, 2 tails], [3 heads, 1 tail] and [4 head, 0 tails] Range of X = Number of possible values it can take (That is, Number of possible heads) So in this case X = {0,1,2,3,4} Option (C) 3) Given, Number of tails = 3, in a total of 4 coin tosses So X = Number of heads = 1 Option (D) 4) Probability = Number of favorable cases/ Total number of cases Here, Favorable case = Getting a heads So, number of favorable cases = 4 (as heads can come in anyone of the four coin tosses) Total cases = 2^4 = 16 Probability = 4/16 = 1/4 Option (B) 5) The term ex-ante is a phrase meaning \"before the event\" So here, Ex ante means stat measure is given before observation is taken. Option(A).