-- Aug 30 In-Class Exercise Thread

* Birthday = Sept 3rd * X is a random variable that maps events HEADS or TAILS to a dollar amount that bob will pay * probability distribution * @BT@Pr(H) = 1/3 @BT@ * @BT@Pr(T) = 2/3 @BT@ * @BT@ EV = (1/3)*$5 + (2/3) * $1 = $2.33@BT@

-- Aug 30 In-Class Exercise Thread

        o	Pr(H) = 1/9
        o	Pr(T) = 8/9

        X : {H,T} -> {5,1}

		          	          = 5 * Pr{H} + 1 * Pr{T}
		                          = 5 * (1/9) + 1 * (8/9)
		                          = 13/9  

• My birthday falls on the 9th • The sample space for the coin toss is S = {H,T} • Probability distribution for the coin toss event is as below: o Pr(H) = 1/9 o Pr(T) = 8/9 • Random variable -> X = Amount Bob pays • X maps the coin toss sample space to the winning amount: X : {H,T} -> {5,1} • Expected value of X = 5 * Pr{X=5} + 1 * P{X=1} = 5 * Pr{H} + 1 * Pr{T} = 5 * (1/9) + 1 * (8/9) = 13/9

-- Aug 30 In-Class Exercise Thread

'''Random var:''' *X(H) = 5 *X(T) = 1 '''Distribution:''' *P(H) = 1/19 *P(T) = 18/19 '''Expected value:''' *E(X) = 1/19 * 5 + 18/19 * 1 = 23/19

-- Aug 30 In-Class Exercise Thread

My Birthday is on 28th of March. P(Heads) = 1/28 [Probability of getting heads for a coin toss] P(Tails) = 27/28 [Probability of getting tails for a coin toss] Let X be the random variable representing the money Bob pays for the coin toss P(X=5) = 1/28 P(X=1) = 27/28 Expected value E(X) = 5*1/28 + 1 * 27/28= 0.1785 + 0.9642 = $1.1427

-- Aug 30 In-Class Exercise Thread

S = {head, tail} P(head) = 1/15 P(tail) = 14/15 randomV(head) = 5 randomV(tail) = 1 payment = sum(P*randomV) payment = 1/15 *5 + 14/15 *1 = $1.267