In Las Vegas, a certain game #1 is described by the random variable X. The PMF i

Question

In Las Vegas, a certain game #1 is described by the random variable X. The PMF is described by P_x[k] = {5999/12000, k = +0.06 5999/12000, k = -0.04 1/6000, k = -50.00 Thus, for this game #1 we win 6 cents if the nickel lands on heads, lose 4 cents if the nickel lands on tails, and we lose $50.00 if the nickel lands on its side In Las Vegas, a certain game #2 is described by the random variable X. The PMF is described by P_x[k] = {5999/12000, k = +0.04 5999/12000, k = -0.07 1/6000, k = +60.00 Thus, for this game #2 we win 4 cents if the nickel lands on heads, lose 7 cents if the nickel lands on tails, and we win $60.00 if the nickel lands on its side a) How much money do we win in game #1 in one day if we play 1000 times? b) How much money do we win in game #2 in one day if we play 1000 times?

Explanation / Answer

a) expected win in one game=(5999/12000)*0.06+(5999/12000)*(-0.04)+(1/6000)*(-50)=0.00167

hence expected win in 1000 games =1000*0.00167 =$1.67

b)

expected win in one game=(5999/12000)*0.04+(5999/12000)*(-0.07)+(1/6000)*(60)=0.005

hence expected win in 1000 games =1000*-0.005 =-$5.00

please revert for doubt

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