prediction of points using random number generator

Question

sandra swims the 100m freestyle for swim team. She gets 3 points for 1st place, 2 for 2nd, 1 for 3rd and 0 points if she doesnt place. her coach used last years stats to design a simulation using a random number generator to predict how many points she would recieve in her first race this season

Integer value points frequency

1-8 3 20

9-15 2 12

16-19 1 6

20 0 2

what is sandras expected value of points awarded for race . Please show work.

Answer 1

Let X represent the RV for points.

Total frequency = 20+12+6+2 = 40

P(X=3) = 20/40

P(X=2) = 12/40

P(X=1) = 6/40

P(X=0) = 2/40

Expected value of points = E(X) = ∑x_iP(X=x_i) = 3(20/40) + 2(12/40) + 1(6/40) + 0(2/40)

=90/40 = 2.25