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Aug 30 In-Class Exercise Thread.

Hi Everyone,

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

Best, Chris

Hi Everyone, Post your solutions to the Aug 30 In-class exercise in this thread. Best, Chris

-- Aug 30 In-Class Exercise Thread

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`

(Edited: 2017-08-30)

My birthday is August 1. '''State Space:''' * @BT@S={Heads, Tails}@BT@ '''Random Variable: ''' * @BT@X[Heads] = 5@BT@ * @BT@X[Tails] = 1@BT@ '''Probability Distribution:''' * @BT@Pr[Heads] = 1/1 = 1@BT@ * @BT@Pr[Tails] = 1 - Pr[Heads] = 0@BT@ '''Expected Value:''' * @BT@E[X] = 5*Pr[Heads] + 1*Pr[Tails] = 5*1 + 1*0 = $5@BT@

-- Aug 30 In-Class Exercise Thread

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`

(Edited: 2017-08-30)

*X = Amount Bob pays * @BT@P(X=5) = p(H) = 1/7@BT@ * @BT@P (X=1) = P(T) = 6/7@BT@ *Expected value = @BT@5*(1/7) + 1*(6/7) = 1.57@BT@

-- Aug 30 In-Class Exercise Thread

Birthdate is 4th.

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

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

-- Aug 30 In-Class Exercise Thread

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

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

(Edited: 2017-08-30)

*S = {head, tail} *P(head) = 1/8 *P(tail) = 7/8 *randomV(head) = 5 *randomV(tail) = 1 *payment = sum(P*randomV) payment = 1/8 *5 + 7/8 *1 = $1.5

-- Aug 30 In-Class Exercise Thread

'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]=5*1/26 + 25/26
E[X]=30/26=15/13
E[X]=$1.15

(Edited: 2017-08-30)

*'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]=5*1/26 + 25/26 *E[X]=30/26=15/13 *E[X]=$1.15

-- Aug 30 In-Class Exercise Thread

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] = 5*P(X=5) + 1*P(X=1)

	= 5/24 + 23/24
	= 28/24

Thus, expected value is $1.67

(Edited: 2017-08-30)

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] = 5*P(X=5) + 1*P(X=1) = 5/24 + 23/24 = 28/24 Thus, expected value is $1.67

-- Aug 30 In-Class Exercise Thread

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 : 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

-- Aug 30 In-Class Exercise Thread

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

(Edited: 2017-08-30)

*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

-- Aug 30 In-Class Exercise Thread

birth date=13

p(H)= 1/13

p(T)= 12/13

E[x]= 5*1/13+1*12/13 = 17/13= $1.307

(Edited: 2017-08-30)

birth date=13 p(H)= 1/13 p(T)= 12/13 E[x]= 5*1/13+1*12/13 = 17/13= $1.307