case study solution_counting and probability

# case study solution_counting and probability - Probability...

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Probability and Random Process Case Study Solution Module 1

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Sample Space Problem 1: Count the number of voice packets containing only silence produced from a group of N speakers in a 10-ms period. Solution: Denote sample space by S then , S = { 0, 1, 2, … , N } Problem 2: A block is transmitted repeatedly over a noisy channel until an error-free block arrives at the receiver. Count the number of transmission required. Solution: Denote sample space by S then , S = { 1, 2, 3, …, }
Sample Space Problem 3: Measure the time between two message arrivals at a message center. Solution: Denote sample space by S then , S = { t: t 0 } = [ 0, ) where t denotes time. Problem 4: Measure the lifetime of a given computer memory chip in a specified environment. Solution: Denote sample space by S then , S = { t: t 0 } = [ 0, ) where t denotes time.

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Events Problem 1: Write the values of events for problems in case study of sample space for following events: 1. No active packets are produced 2. Fewer than 10 transmission are required 3. Less than t 0 seconds elapse between message arrivals 4. The chip lasts for more than 1000 hours but fewer than 5000 hour Solution : 1. No active packets are produced, then A = { 0 }
Events 2. Fewer than 10 transmission are required A = { 1, 2, … , 9 } 3. Less than t 0 seconds elapse between message arrivals A = { t : 0 t < t 0 } = [ 0, t 0 ) 4. The chip lasts for more than 1000 hours

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Events Problem 2: Measure the lifetime of a given computer memory chip in a specified environment. Let the events A, B, and C be defined by A=(5, ), B = (7, ) and C = (0,3]. Describe these events in words. Find the events A B, A C, and A B and describe them in words. Solution: A = ( 5 , ) lifetime is greater than 5 B = ( 7 , ) Lifetime is greater then 7 C = ( 0 , 3 ] Lifetime is not greater than 3 A B = ( 7 , ) Lifetime is greater than 5 and 7 A C = Lifetime is greater than 5 and not greater than 3 A B = ( 5 , ) Lifetime is greater than 5 or 7
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case study solution_counting and probability - Probability...

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