AMS 311 - Probability Mass Function

AMS 311 - Probability Mass Function - ! Let S be a discrete...

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DR. DOUGLAS H. JONES ±²³´µ¶·¶¸¶¹º²»¼»´½´¾¿¶À¼ÁÁ¶ÂÃĵ¾´²Ä ž¼¾´Á¾´µÁ¶Æ²º¶À¼Ä¼ÇȺÁ ÉÃÄȶÊ˶ÌÍÍÍ Î¼Äϲ ¶!¼º´¼»½È Let S be a discrete sample space with the set of elementary events denoted by E = {e i , i = 1, 2, 3…}. A random variable is a function Y(e i ) that assigns a real value to each elementary event, e i . The random variable is denoted by Y. The set of all possible values of Y is the set {y i = Y(e i ), i = 1, 2, 3…}. The set of all possible values of Y is a finite or countably infinite set, and Y is said to be a discrete random variable. Let y be the set of values of Y. The subset of all elementary events that are assigned the y, is the compound event {e i : Y(e i ) = y}. Usually the probabilities of all the elementary events are known, therefore the probability of this compound event can be readily computed by summing over all the elementary events. Toss a coin twice. Let Y denote the number of heads. Denote (Tail, Tail) to be the elementary event that the first toss is tail and the second toss is tail. Denote the other elementary events accordingly. Compound Event Elementary Events (Y=0) (Tail, Tail) (Y=1) (Tail, Head), (Head, Tail) (Y=2) (Head, Head)
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DR. DOUGLAS H. JONES ±²³´µ´¶·¶¸¹º»µ¼¼º½¾¿À¸¶³¿ Let Y be a discrete random variable. A probability mass function is f(y) = P{e i : Y(e i ) = y}. It is a function with values between 0 and 1 and whose sum is 1 over all values of y. Toss a balanced coin once. Let Y be the number of heads that occurs. Find the probability mass function of Y.
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AMS 311 - Probability Mass Function - ! Let S be a discrete...

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