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-- Aug 30 In-Class Exercise Thread

Birthday - August 24

Pr(Head) = 1/24 Pr(Tail) = 23/24

Expected value = 5*(1/24) + 1*(23/24) = $1.16

Birthday - August 24 Pr(Head) = 1/24 Pr(Tail) = 23/24 Expected value = 5*(1/24) + 1*(23/24) = $1.16

-- Aug 30 In-Class Exercise Thread

BirthDay = 25 S = {head, tail}

P(X = head) = P(H) = 1/25 = 0.04 P(X = tail) = P(T) = 24/25 = 0.96 randomV(head) = 5 random(tail) = 1

Expected Value (i.e payment) = 5 * (1/25) + 1 (24/25) = 1.16

BirthDay = 25 S = {head, tail} P(X = head) = P(H) = 1/25 = 0.04 P(X = tail) = P(T) = 24/25 = 0.96 randomV(head) = 5 random(tail) = 1 Expected Value (i.e payment) = 5 * (1/25) + 1 (24/25) = 1.16

-- Aug 30 In-Class Exercise Thread

Birthday : 8 Sample space : {H, T} Random variable: X
X[H] = 5 X[T] = 1
Pr(H) = 1/8 Pr(T) = 7/8 E(X) = 5*(1/8) + 1(7/8) = 1.5

'''Birthday : 8 Sample space : {H, T} Random variable: X X[H] = 5 X[T] = 1 Pr(H) = 1/8 Pr(T) = 7/8 E(X) = 5*(1/8) + 1(7/8) = 1.5'''

-- Aug 30 In-Class Exercise Thread

My birthday on 27 P(H) = 1/27 P(T) = 26/27

Distribution : P(H): 4.17 P(T): 95.83

Expected value : 5*(1/27)+1(26/27)

My birthday on 27 P(H) = 1/27 P(T) = 26/27 Distribution : P(H): 4.17 P(T): 95.83 Expected value : 5*(1/27)+1(26/27)

-- Aug 30 In-Class Exercise Thread

P(H) = 1/14
P(T) = 13/14
`P_r(X=H)` = 1/14*5
`P_r(X=T)` = 13/14*1
`E[x]` = `P_r(X=H)` + `P_r(X=T)` = 18/14

(Edited: 2017-08-30)

* P(H) = 1/14 * P(T) = 13/14 * @BT@P_r(X=H)@BT@ = 1/14*5 * @BT@P_r(X=T)@BT@ = 13/14*1 * @BT@E[x]@BT@ = @BT@P_r(X=H)@BT@ + @BT@P_r(X=T)@BT@ = 18/14

-- Aug 30 In-Class Exercise Thread

Birth Day : 10th
p(H) : 1/10
p(T): 9/10
E(x) = (5*1/10) + (1 * 9/10) = 14/10 = 1.4

* Birth Day : 10th * p(H) : 1/10 * p(T): 9/10 * E(x) = (5*1/10) + (1 * 9/10) = 14/10 = 1.4

-- Aug 30 In-Class Exercise Thread

My birthday is May 10

Sample space: {Heads, Tails}

Random variables: X[Heads] = 5 X[Tails] = 1

Probability Distribution: Pr[Heads] = 1/10 Pr[Tails] = 1 - Pr[Heads] = 9/10

Expected value: 5*(1/10) + 1*(9/10) = 14/10 = 7/5

My birthday is May 10 Sample space: {Heads, Tails} Random variables: X[Heads] = 5 X[Tails] = 1 Probability Distribution: Pr[Heads] = 1/10 Pr[Tails] = 1 - Pr[Heads] = 9/10 Expected value: 5*(1/10) + 1*(9/10) = 14/10 = 7/5

-- Aug 30 In-Class Exercise Thread

Brithday is Nov 28

Random variable X=The amount that Bob pays,

S={head, tail},

X(h)=5 if X is head,

X(t)=1 if X is tail,

Pr(head)=1/28

Pr(tail)=1-1/28=27/28

E(X)=X(h)*Pr(X(h))+X(t)*Pr(X(t))=5*1/28+1*(1-1/28)=8/7

(Edited: 2017-08-30)

Brithday is Nov 28 Random variable X=The amount that Bob pays, S={head, tail}, X(h)=5 if X is head, X(t)=1 if X is tail, Pr(head)=1/28 Pr(tail)=1-1/28=27/28 E(X)=X(h)*Pr(X(h))+X(t)*Pr(X(t))=5*1/28+1*(1-1/28)=8/7

-- Aug 30 In-Class Exercise Thread

My birth date is 22nd April.

P(Heads) = 1/22
P(Tails) = 21/22

Expected Value = 5(1/22) + 1(21/22) = 1.17

My birth date is 22nd April. *P(Heads) = 1/22 *P(Tails) = 21/22 *Expected Value = 5(1/22) + 1(21/22) = 1.17

-- Aug 30 In-Class Exercise Thread

Birthdate: 23 S: {H, T} P(H) = 1/23 P(T) = 22/23

Random variable (X) = Money Bob pays.

Expected amount = 5*P(H) + 1*P(T) = 5*1/23 + 1*22/23 = 27/23

(Edited: 2017-08-30)

Birthdate: 23 S: {H, T} P(H) = 1/23 P(T) = 22/23 Random variable (X) = Money Bob pays. Expected amount = 5*P(H) + 1*P(T) = 5*1/23 + 1*22/23 = 27/23