If A shows a head the man scores 1 point, if B shows a head he scores 2 points and if Cshows a head he scores 3 points. Calculate the expectation of his score.
2007-04-01 03:06:13 · 9 answers · asked by kev_xinx 1 in Science & Mathematics ➔ Mathematics
I assume he scores zero points for not getting a head. Since expectation is linear, this boils down to adding the expected points for each coin, ie.
½*1 + ½*0 + ½*2 + ½*0 + ½*3 + ½*0
= ½ + 0 + 1 + 0 + 3/2 + 0
= 3.
2007-04-01 03:19:24 · answer #1 · answered by MHW 5 · 1⤊ 0⤋
1/2*1+ 1/2*2+1/2*3
=3
2007-04-01 10:43:30 · answer #2 · answered by yahoooo 2 · 0⤊ 0⤋
1/24
1/2*1/2*1/2 for all the heads and tails
and times it by 1/3 for the coins
2007-04-01 11:25:05 · answer #3 · answered by Ktik 2 · 0⤊ 0⤋
Expectation of his score is
E = 1 * Pr(A head) + 2 * Pr(B head) + 3 * Pr(C head)
Pr of each getting heads is 1/2, so
E = 1*(1/2) + 2*(1/2) + 3*(1/2) = 6*(1/2) = 3
2007-04-01 10:14:56 · answer #4 · answered by David K 3 · 2⤊ 0⤋
Very simple, 1/2 * 1 + 1/2 * 2 + 1/2 * 3
Which you probably already know is 3 lol
2007-04-01 10:41:50 · answer #5 · answered by biglildan 6 · 0⤊ 0⤋
the lowest score he will get is 0 and the highest is 6
2007-04-01 10:34:14 · answer #6 · answered by tyroneskee 2 · 0⤊ 0⤋
3?
2007-04-01 10:13:34 · answer #7 · answered by crazy_for_writing 4 · 1⤊ 0⤋
0 points P = 0.125 (TTT)
1 point P = 0.125 (HTT)
2 points P = 0.125 (THT)
3 points P = 0.250 (HHT) or (TTH)
4 points P = 0.125 (HTH)
5 points P = 0.125 (THH)
6 points P = 0.125 (HHH)
Scoring 3 is highest probability, but only has 25% chance of occurring.
Ah
Expected Value
= sum of probabilities X payoff
= 0.125 + 2(0.125) + 3(0.25) + 4(0.125) + 5(0.125) + 6(0.125)
= 3
2007-04-01 10:16:44 · answer #8 · answered by Orinoco 7 · 0⤊ 2⤋
8 outcomes:
throws score
HHH 6
HHT 3
HTH 4
HTT 1
THH 5
THT 2
TTH 3
TTT 0
Total =24
Expectation=Total/8=24/8=3
2007-04-01 10:17:42 · answer #9 · answered by Adam B 2 · 1⤊ 0⤋