b***k
发帖数: 2673 | 1 ☆─────────────────────────────────────☆
l00 (100) 于 (Sat Oct 20 14:11:04 2007) 提到:
1. X is normally distributed N(0,1)
what is the distribution density function of Y=X^2
2. throw two dices, let random valuable X = sum of the two dices.
Now, let you throw these two dices at most 30 times, you can stop at any
time during 30 times, your profit will be only related to the last dicing
result X.
how to maxmise your profix (or X).
☆─────────────────────────────────────☆
everforget (yy) 于 (Sat | c********8
发帖数: 2 | 2 Define Y[n]=E{max(X[n],X[n+1], ...., X[30])}, then Y[n]=E(max(X[n],Y[n+1])).
prob[2]=1/36=0.0277778
prob[3]=2/36=0.0555556
prob[4]=3/36=0.0833333
prob[5]=4/36=0.111111
prob[6]=5/36=0.138889
prob[7]=6/36=0.166667
prob[8]=5/36=0.138889
prob[9]=4/36=0.111111
prob[10]=3/36=0.0833333
prob[11]=2/36=0.0555556
prob[12]=1/36=0.0277778
Y[30]=E(max(X[30]))=E(X[30])=7;
Recursively,
Y[n]=E(max(X[n],Y[n+1]))=sum{max(X[n],Y[n+1])*prob(X[n])}
Y[1]=11.1289
Y[2]=11.104
Y[3]=11.0784
Y[4]=11.052
Y[5]=11.025
Y[6]=10
【在 b***k 的大作中提到】
: ☆─────────────────────────────────────☆
: l00 (100) 于 (Sat Oct 20 14:11:04 2007) 提到:
: 1. X is normally distributed N(0,1)
: what is the distribution density function of Y=X^2
: 2. throw two dices, let random valuable X = sum of the two dices.
: Now, let you throw these two dices at most 30 times, you can stop at any
: time during 30 times, your profit will be only related to the last dicing
: result X.
: how to maxmise your profix (or X).
: ☆─────────────────────────────────────☆
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