Question

The payoff table for three possible courses of action is given below. Which of the three actions will produce the largest expected value? What is it?

	A1	A2	A3
Pi	Xi	Xi	Xi
.35	$300	$400	$500
.30	$1,100	$1,200	$1,000
.15	$1,200	$1,700	$1,800
.20	$400	$4,200	$800

Answer 1

Se let payoff tu us consider the following LA A A 0.35 0.30 0.15 0.20 $300 $1100 $1200 $400 $400 $1200 $1900 $4,200 $500 $ 1000 $1800 $800 If the poobability distoibution for the fandom voiable , x x x...... an - Po P P2 ....... Pn. Where Po=P() we define the expected value of x, denoted. EC *), by the foomula. E(X) = x, Pi + X2 Px +.....+ XnPn. Let the expected values of the action A,,A₃ & A3 be ECAI), E (A») & E(A3). The expected values for the action A can be calculated al E(Al) = 10.35 x 300)+(0.30 x 1100) + (0,15 x/2008+ (0-20X400) = 105+ 330+180+80 ECAI) - 695 he expected value for the action Ay can be calo E(A)= (0.35X400) +10.30 X 1200)+(0.15x1700).-(0.20x4200) = 140+ 360+255 + 840 E(A2) = 1595 The expected valere for the action nz can be calculated a 1 E(A3)= (0.35 X 500) + (0.30x1000) + (0.15X1800)+ (0-20x800) = 175 +300+ 270+ 160 = 905 Thus, we can see that Icongest expected value and the action A, will produce the the value is $1595