I'm really confused with the conditioning that must be going on in this question. Is this the way to set this question up in the beginning? I follow the rest of the model solution if all of this is true, but I sense this is wrong, please tell me where it is wrong:
First, we need to get the conditional probabilities of rural|group and urban|group for each of the two groups.
Business
E[Business)=1.8=E[Business|Rural]P(Rural|Business)+E[Business|Urban]P(Urban|Business)
Since given business, your either Rural or Urban, that means
1=P(Rural|Business)+P(Urban|Business)
E[Business)=1.8=1.0*P(Rural|Business)+2.0*(1-P(Rural|Business))
P(Rural|Business)=-(1.8-2)=0.2, which implies P(Urban|Business)=0.8
Pleasure
E[Pleasure]=2.3=E[Pleasure|Rural]P(Rural|Pleasure)+E[Pleasure|Urban]P(Urban|Pleasure)
Since given pleasure, your either Rural or Urban, that means
1=P(Rural|Pleasure)+P(Urban|Pleasure)
E[Pleasure)=2.3=1.5*P(Rural|Pleasure)+2.5*(1-P(Rural|Pleasure))
P(Rural|Pleasure)=-(2.3-2.5)=0.2, which implies P(Urban|Pleasure)=0.8
Then, we need to get the joint distribution probabilities from the conditional probabilities we attained above.
Business
0.2=P(Rural|Business)=P(Rural intersect Business)/P(Business)
Since there are equal number of business and pleasure, P(Business)=0.5
P(Rural intersect Business)=0.2*0.5=0.1
0.8=P(Urban|Business)=P(Urban intersect Business)/P(Business)
P(Urban intersect Business)=0.8*0.5=0.4
Pleasure
0.2=P(Rural|Pleasure)=P(Rural intersect Pleasure)/P(Pleasure)
Since there are equal number of business and pleasure, P(Pleasure)=0.5
P(Rural intersect Pleasure)=0.2*0.5=0.1
0.8=P(Urban|Pleasure)=P(Urban intersect Pleasure)/P(Pleasure)
P(Urban intersect Pleasure)=0.8*0.5=0.4
Now, u=E(claims|joint selection)
u=E[Business|Rural]*P(Rural intersect Business)+E[Business|Urban]*P(Business intersect Urban]+E[Pleasure|Rural]*P(Rural intersect Pleasure)+E[Pleasure|Urban]*P(Pleasure intersect Urban]=1.0*0.1+2.0*0.4+1.5*0.1+2.5*0.4=2.05
First, we need to get the conditional probabilities of rural|group and urban|group for each of the two groups.
Business
E[Business)=1.8=E[Business|Rural]P(Rural|Business)+E[Business|Urban]P(Urban|Business)
Since given business, your either Rural or Urban, that means
1=P(Rural|Business)+P(Urban|Business)
E[Business)=1.8=1.0*P(Rural|Business)+2.0*(1-P(Rural|Business))
P(Rural|Business)=-(1.8-2)=0.2, which implies P(Urban|Business)=0.8
Pleasure
E[Pleasure]=2.3=E[Pleasure|Rural]P(Rural|Pleasure)+E[Pleasure|Urban]P(Urban|Pleasure)
Since given pleasure, your either Rural or Urban, that means
1=P(Rural|Pleasure)+P(Urban|Pleasure)
E[Pleasure)=2.3=1.5*P(Rural|Pleasure)+2.5*(1-P(Rural|Pleasure))
P(Rural|Pleasure)=-(2.3-2.5)=0.2, which implies P(Urban|Pleasure)=0.8
Then, we need to get the joint distribution probabilities from the conditional probabilities we attained above.
Business
0.2=P(Rural|Business)=P(Rural intersect Business)/P(Business)
Since there are equal number of business and pleasure, P(Business)=0.5
P(Rural intersect Business)=0.2*0.5=0.1
0.8=P(Urban|Business)=P(Urban intersect Business)/P(Business)
P(Urban intersect Business)=0.8*0.5=0.4
Pleasure
0.2=P(Rural|Pleasure)=P(Rural intersect Pleasure)/P(Pleasure)
Since there are equal number of business and pleasure, P(Pleasure)=0.5
P(Rural intersect Pleasure)=0.2*0.5=0.1
0.8=P(Urban|Pleasure)=P(Urban intersect Pleasure)/P(Pleasure)
P(Urban intersect Pleasure)=0.8*0.5=0.4
Now, u=E(claims|joint selection)
u=E[Business|Rural]*P(Rural intersect Business)+E[Business|Urban]*P(Business intersect Urban]+E[Pleasure|Rural]*P(Rural intersect Pleasure)+E[Pleasure|Urban]*P(Pleasure intersect Urban]=1.0*0.1+2.0*0.4+1.5*0.1+2.5*0.4=2.05
Exam C Sample #70