Assignment (Solutions of problems 1 tobbcr.uwaterloo.ca/~lcai/ece418/solution_1.pdf · Assignment #...

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Assignment # 1 (Solutions of problems 1 to 4) Problem #1 Solution: Problem #2 Solution: P(τ 10 >2) = e 2λ = e 2 Problem #3 Solution: What is the probability that a customer will spend more than 15 minutes in the bank? P(X>15) = e –15λ =e 3/2 . Given that the customer is still in the bank after 10 minutes, what is the probability that she will spend more than 15 minutes in the bank? Since the exponential distribution does not ‘remember’ that the customer has already spent 10 minutes in the bank, this is equivalent to the probability that the entering customer spends at least 5 minutes in the bank, given that she is still in the bank for 10 minutes. P(X>5) = e –5λ =e –1/2 . What is the probability that she will spend another 15 minutes in the bank? P(X>15) = e –15λ =e –3/2

Transcript of Assignment (Solutions of problems 1 tobbcr.uwaterloo.ca/~lcai/ece418/solution_1.pdf · Assignment #...

Page 1: Assignment (Solutions of problems 1 tobbcr.uwaterloo.ca/~lcai/ece418/solution_1.pdf · Assignment # 1 (Solutions of problems 1 to 4) Problem #1 Solution: Problem #2 Solution: P(τ10>2)

Assignment # 1 

(Solutions of problems  1 to 4) 

Problem  #1 

Solution: 

 

Problem  #2 

Solution: 

P(τ10>2) = e ‐2λ = e ‐2 

Problem  #3 

Solution:      

• What is the probability that a customer will spend more than 15 minutes in the bank?  

P(X>15) = e –15λ = e –3/2. 

• Given that the customer is still in the bank after 10 minutes, what is the probability that she will spend more than 15 minutes in the bank? 

Since the exponential distribution does not ‘remember’ that the customer has already spent 10 minutes in the bank, this is equivalent to the probability that the entering customer spends at least 5 minutes in the bank, given that she is still in the bank for 10 minutes. 

P(X>5) = e –5λ = e –1/2. 

• What is the probability that she will spend another 15 minutes in the bank?  

P(X>15) = e –15λ = e –3/2 

 

 

 

Page 2: Assignment (Solutions of problems 1 tobbcr.uwaterloo.ca/~lcai/ece418/solution_1.pdf · Assignment # 1 (Solutions of problems 1 to 4) Problem #1 Solution: Problem #2 Solution: P(τ10>2)

 

Problem  #4 

Solution:      

 

 

Page 3: Assignment (Solutions of problems 1 tobbcr.uwaterloo.ca/~lcai/ece418/solution_1.pdf · Assignment # 1 (Solutions of problems 1 to 4) Problem #1 Solution: Problem #2 Solution: P(τ10>2)

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Page 5: Assignment (Solutions of problems 1 tobbcr.uwaterloo.ca/~lcai/ece418/solution_1.pdf · Assignment # 1 (Solutions of problems 1 to 4) Problem #1 Solution: Problem #2 Solution: P(τ10>2)

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Page 6: Assignment (Solutions of problems 1 tobbcr.uwaterloo.ca/~lcai/ece418/solution_1.pdf · Assignment # 1 (Solutions of problems 1 to 4) Problem #1 Solution: Problem #2 Solution: P(τ10>2)

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Page 7: Assignment (Solutions of problems 1 tobbcr.uwaterloo.ca/~lcai/ece418/solution_1.pdf · Assignment # 1 (Solutions of problems 1 to 4) Problem #1 Solution: Problem #2 Solution: P(τ10>2)

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