(b) A point Y is chosen randomly from the interval (0, 1). Another point X is then chosen randomly from the interval (0, Y). Find P(X

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(b) A point Y is chosen randomly from the interval (0, 1). Another point X is then chosen randomly<br>from the interval (0, Y). Find P(X < a|Y = y) and E[X|Y = y].<br>(c) Independent Bernoulli trials, of success probability p, are continually performed until the first<br>success is achieved. Let X be the number of trials needed to obtain the first success. Let<br>1, if the first trial results in success;<br>Y =<br>0,<br>otherwise.<br>Find E[tX|Y = i] for i = 0, 1. Hence, or otherwise, compute E[t*].<br>

Extracted text: (b) A point Y is chosen randomly from the interval (0, 1). Another point X is then chosen randomly from the interval (0, Y). Find P(X < a|y="y)" and="" e[x|y="y]." (c)="" independent="" bernoulli="" trials,="" of="" success="" probability="" p,="" are="" continually="" performed="" until="" the="" first="" success="" is="" achieved.="" let="" x="" be="" the="" number="" of="" trials="" needed="" to="" obtain="" the="" first="" success.="" let="" 1,="" if="" the="" first="" trial="" results="" in="" success;="" y="0," otherwise.="" find="" e[tx|y="i]" for="" i="0," 1.="" hence,="" or="" otherwise,="" compute="">

Jun 10, 2022

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(b) A point Y is chosen randomly from the interval (0, 1). Another point X is then chosen randomly from the interval (0, Y). Find P(X

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