Answers are ecb Please provide explanations The next three q

The next three questions use the following joint probability table. Fill in the missing values What is the value of G What is the value of P[A=5|S=40] Calculate the expected value of A, conditional on S=40. That is, E[A|S=40]=

Solution

15.

we known that sum of all probabilities is one

P(S=s)=1

P(S=30)+P(S=40)+P(S=50)=1

0.35+P(S=40)+0.15=1

P(S=40)=0.5

P(A=a)=1

P(A=5)+P(A=10)=1

P(A=10)=1-0.4=0.6

The probability is

P(A=10,S=40)=P(A=10)-[P(A=10,S=30)+P(A-10, S=50)]

                      =0.6-[0.3+0.1]

                      =0.2

The G is

G=P(A=5,S=40)=P(S=40)-P(A=10,S=40)

                         =0.5-0.2

                        =0.3

16.

P[A=5|S=40]=P[A=5,S=40]/P[S=40]

                   =0.3/0.5

                 =0.6

17

E[A|S=40]=5*P[A=5|S=40]+10*P[A=10|S=40]

               =5*0.6+10*(0.2/0.5)

               =3+4

               =7

	S=30	S=40	S=50	P(A=a)
A=5	0.05	0.3	0.05	0.4
A=10	0.3	0.2	0.1	0.6
P(S=s)	0.35	0.5	0.15	1