Hi Everyone,

Post your solutions to the Aug 30 In-class exercise in this thread.

Best, Chris

My birthday is August 1.

'''State Space:'''

• S={Heads, Tails}

'''Random Variable: '''

• X[Heads] = 5
• X[Tails] = 1

'''Probability Distribution:'''

• Pr[Heads] = 1/1 = 1
• Pr[Tails] = 1 - Pr[Heads] = 0

'''Expected Value:'''

• E[X] = 5*Pr[Heads] + 1*Pr[Tails] = 5*1 + 1*0 = $5

*X = Amount Bob pays

• P(X=5) = p(H) = 1/7
• P (X=1) = P(T) = 6/7

*Expected value = 5*(1/7) + 1*(6/7) = 1.57

Birthdate is 4th.

Pr(pay=5) = 1/4, Pr(pay=1) = 3/4. Therefore, expected value = 5/4 + 3/4 = 2

*S = {head, tail} *P(head) = 1/8 *P(tail) = 7/8 *randomV(head) = 5 *randomV(tail) = 1

payment = sum(PrandomV) payment = 1/8 *5 + 7/8 *1 = $1.5

*'X= total money received from Bob.' *P(Heads)=1/26 *P(Tails)=25/26 *Xh=5 *Xt=1 *The expected amount to receive from Bob *E[X]= Xh * p(Heads) + Xt * p(Tails) E[X]=51/26 + 25/26 *E[X]=30/26=15/13 *E[X]=$1.15

My Birthday is on 24.

So, P(H) = 1/24

P(T) = 23/24

Let X be the random variable corresponding to the money Bob pays. Then, by the given statement:

X = {5, 1}

P(X=5) = P(H) = 1/24

P(X=1) = P(T) = 23/24

E[X] = 5P(X=5) + 1P(X=1) = 5/24 + 23/24 = 28/24

Thus, expected value is $1.67

Birthday : 20

S:{heads, tails} Pr_Head=1/20 Pr_Tail=1-Pr_Head Pr_Tail=19/20 Val=5*(Pr_Head)+1*(Pr_Tail) Val=5*1/20+19/20 Val=1.35

*Birthday = July 4 *Random Variable X *Sample Space: H, T

• X[Head] = $5
• X[Tail] = $1

Probability Distribution: *P(H) = 0.25 *P(T) = 0.75

Expected Value: *E(X) = 5 * 0.25 + 1 * 0.75 = $2

birth date=13

p(H)= 1/13

p(T)= 12/13

E[x]= 51/13+112/13 = 17/13= $1.307