Expected Value Exercise 6
Randy and Samantha are shopping for new cars (one
each). Randy expects to pay $15,000 with 1/5 probability and $20,000 with 4/5
probability. Samantha expects to pay $12,000 with 1/4 probability and $20,000
with 3/4 probability.
What is Randy's expected expense for his car?
What is Samantha's expected expense for her car?
EU of randy= probability x price ($)
ReplyDelete---> (1/5x15,000)+(4/5x20,000)= 19,000
EU of samantha= probability x price ($)
---> (1/4x12,000)+(3/4x20,000=18,000
so the expected expense of randy is higher than samantha's
RANDY :
ReplyDeleteprobability 1 = 1/5 = 0.2
X1 =15,000
probability 2 = 4/5 = 0,8
X2 = 20,000
EV = (probability1 x X1) + (probability2 x X2)
= (0.2 x 15,000) + (0,8 x 20,000) = 19,000
SAMANTHA :
probability 1 = 1/4 = 0.25
X1 =12,000
probability 2 = 3/4 = 0,75
X2 =20,000
EV = (probability1 x X1) + (probability2 x X2)
= (0.25 x 12,000) + ( 0,75 x 20,000) = 18,000
Randy expectation
ReplyDelete1/5 (0.20) to pay $15.000
4/5 (0.80) to pay $20.000
Expected Value/EV : (1st Pr) (1st Val) + (2nd Pr) (2nd Val)
EV :(0.20)($15.000) + (0.80) ($20.000) = 3000+16000 = $19.000
so, Randy Expected Expense for his new car is $19.000
Samantha expectation
1/4 (0.25) to pay $12.000
3/4 (0.75) to pay $20.000
Expected Value/EV : (1st Pr) (1st Val) + (2nd Pr) (2nd Val)
EV : (0.25)($12.000)+(0.75)($20.000)= 3000 + 15000 = $18.000
and Samantha Expected expense for her new car is $18.000
Known:
ReplyDeleteRandy and Samantha are shopping new cars. These are both from their own believes :
Randy
1stProbability to pay $ 15,000 is 1/5 = 0.2
2ndProbability to pay $ 20,000 is 4/5 = 0.8
Solution:
Randy’s Expected Value = (1st payment) (1stProbability) + (2nd payment) (2ndProbability)
= ( $ 15,000 * 0.2 ) + ( $ 20,000 x 0.8 )
= $ 3,000 + 16,000
= $ 19,000
Samantha
1stProbability to pay $ 12,000 is 1/4 = 0.25
2ndProbability to pay $ 20,000 is 3/4 = 0.75
Solution:
Samantha’s Expected Value = (1st payment) (1stProbability) + (2nd payment) (2ndProbability)
= ( $ 12,000 * 0.25 ) + ( $ 20,000 x 0.75 )
= $ 3,000 + 15,000
= $ 18,000
So, Randy’s Expected Value is $ 19,000 and Samantha’s Expected Value is $ 18,000
outcomes probability
ReplyDeleteRANDY $ 15,000 1/5 = 0,2
$ 20,000 4/5 = 0,8
SAMANTHA $ 12,000 1/4 = 0,25
$ 20,000 3/4 = 0,75
Expected Expense for Randy
E(x) = (P1 x X1) + (P2 x X2)
= (0,2 x 15,000) + (0,8 x 20,000)
E(x) = $19
Expected Expense for Samantha
E(x) = (P1 x X1) + (P2 x X2)
= (0,25 x 12,000) + (0,75 x 20,000)
E(x) = $18
the expected expense for randy $19 and Samantha is $ 18, so the expected expense randy is greater than samantha.
ANSWER:
ReplyDeleteRandy = 1/5 x 15,000 + 4/5 x 20,000 = 19,000
Samantha = ¼ x 12,000 + ¾ x 20,000 = 18,000