#intermediate nodes count 25 15 10 1 2 3 Table Q4: # intermediate nodes traversed by...

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#intermediate nodes count 25 15 10 1 2 3 Table Q4: # intermediate nodes traversed by 50 messages successfully delivered from A to B Q4. On average 1000 messages per day are successfully delivered from A to B across the network shown in Figure Q3. The engineer would like to define a random variable X as the number of intermediate nodes that a message successfully delivered from A to B will pass through. To do so, they trace 50 messages that are successfully delivered from A to B, and record the number of intermediate nodes each message passes through. The results are summarised in Table Q4. (a) Presuming that X is a discrete random variable, use the sample information to determine the cumulative distribution function, mean and variance of X. Is the sample-size of 50 messages appropriate? Why/Why not? (b) X can also be modelled as a continuous random variable, with a normal distri- bution that has the same mean and variance as the sample. Is this appropriate? Why/Why not? Support your answer by evaluating the cumulative distribution function for the values x = 1, 2 and 3 and comparing it with the discrete cumu- lative distribution function from Q4.a. 10 marks 10 marks #intermediate nodes count 25 15 10 1 2 3 Table Q4: # intermediate nodes traversed by 50 messages successfully delivered from A to B Q4. On average 1000 messages per day are successfully delivered from A to B across the network shown in Figure Q3. The engineer would like to define a random variable X as the number of intermediate nodes that a message successfully delivered from A to B will pass through. To do so, they trace 50 messages that are successfully delivered from A to B, and record the number of intermediate nodes each message passes through. The results are summarised in Table Q4. (a) Presuming that X is a discrete random variable, use the sample information to determine the cumulative distribution function, mean and variance of X. Is the sample-size of 50 messages appropriate? Why/Why not? (b) X can also be modelled as a continuous random variable, with a normal distri- bution that has the same mean and variance as the sample. Is this appropriate? Why/Why not? Support your answer by evaluating the cumulative distribution function for the values x = 1, 2 and 3 and comparing it with the discrete cumu- lative distribution function from Q4.a. 10 marks 10 marks

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A a The cumulative distribution function of X is determined by calculating the cumulative frequency ... View the full answer