The time T between requests to a web server is exponentially distributed with mean 0.5 seconds....

The time T between requests to a web server is exponentially distributed with mean 0.5 seconds.

(a) What is the value of the parameter in this exponential distribution? Give the p.d.f. and c.d.f. of T? [2]

(b) Use the c.d.f. of T to find the median request time and interpret it. [3]

(c) What is the probability that the request time is between 0.25 and 1.5 seconds? [1](

d) Find the 60th percentile of the request time and interpret it. [2]

Expert Solution

orchestra answered 1 year ago

the time between phone calls received by a telephonist is exponentially distributed with a mean of...

the time between phone calls received by a telephonist is exponentially distributed with a mean of 10 minutes.what is the probability that there are no more than four calls within one hour?

Let N be the number of requests to a web server per day and let N...

Let N be the number of requests to a web server per day and let N Poisson(). Each request comes from a human with probability p or from a spam bot with probability 1 ? p. Assume that the requests are independent of each other. Let X be the number of requests from humans per day and Y be the number of requests from spam bots per day. (a) State the conditional distribution of X given N = n, and...

The distance between flaws on a long cable is exponentially distributed with a mean of 12...

The distance between flaws on a long cable is exponentially distributed with a mean of 12 m. a) Find the probability that the distance between two flaws is greater than 15 m. b) Find the probability that the distance between two flaws is greater than 25 m given that it is greater than 10 m. c) Find the probability that the distance between two flaws is greater than 20 m given that it is greater than 10 m.

Discuss the main similarity and difference between a dedicated web server and a co-located web server....

Discuss the main similarity and difference between a dedicated web server and a co-located web server. Group of answer choices Both of them are mainly used for small to medium-size web sites. Both of them are mainly used for large to enterprise-size web sites. Both of them are kept and connected to the Internet at the web host provider's location. One of them is kept and connected to the Internet at the web host provider's location, while the other is...

Will rate answer 1) Assume a user requests a large object from a web server. Assume...

Will rate answer 1) Assume a user requests a large object from a web server. Assume that for the TCP running on the web server: • the MSS is 1,460 bytes (a more precise value for TCP when operating over an Ethernet), • each segment transmitted contains 66 bytes of headers (for TCP and all lower-level protocols), and • flow and congestion control mechanisms do not limit the rate at which the web server transmits data. a) Derive an expression...

1) The waiting time at an elevator is uniformly distributed between 30 and 200 seconds. What...

1) The waiting time at an elevator is uniformly distributed between 30 and 200 seconds. What is the probability a rider waits less than two minutes? A) 0.4706 B) 0.5294 C) 0.6000 D) 0.7059 2) For any normally distributed random variable with mean μ and standard deviation σ, the percent of the observations that fall between [μ - 2σ, μ + 2σ] is the closest to ________. A) 68% B) 68.26% C) 95% D) 99.73% 3) Which of the following...

Lifetime of certain device is exponentially distributed random variable T( λ ). Probability that T >...

Lifetime of certain device is exponentially distributed random variable T( λ ). Probability that T > 10 is e-3: P{ T> 10} = e-3 The system consists of 6 devices of such type and is in working condition if all of its components are in working condition. a) Find expectation μx and standard deviation σx for given distribution. b) Find the probability that the system will not fail I) in the next 3 years? II) in the next 8 years?...

given an exponentially distributed population with a mean of 385.06 what is the probability of the...

given an exponentially distributed population with a mean of 385.06 what is the probability of the average of 138 randomly selected items being less than 53018.8

Reaction times are normally distributed with mean 100 seconds and standard deviation of 10 seconds. a)...

Reaction times are normally distributed with mean 100 seconds and standard deviation of 10 seconds. a) What is the probability that a randomly chosen individual has reaction time of more than 45 seconds? b) In a random sample of 36 individuals from the above population of reaction times, what is the probability that the sample mean reaction time is more than 45 seconds

Suppose the life time of a certain brand of light bulbs is exponentially distributed with an...

Suppose the life time of a certain brand of light bulbs is exponentially distributed with an average of 1000 hours. a. What’s the probability that a new light bulb won’t be able to reach this amount of time? b. What’s the probability that a new light bulb will have a life between 1000 and 2000 hours? c. Given that a light bulb has been working for 1000 hours, what’s the probability that it can work for another 2000 hours or...

Question