A web server receives 30,000 requests per hour. a. What is the probability that

Question

A web server receives 30,000 requests per hour. a. What is the probability that exactly 50 requests will be received in the next 10 seconds? b. What is the probability that the time between any two requests will be greater than 100 milliseconds? A complex pump has an exponential MTTF of 2 years (continuous 24/7 operation). a. What is probability it will fail within 6 months? b. The pump has now been in operation for 3 years without failure. What is the probability it will fail within the next 2 years? c. The pump just failed, but I had one spare in my maintenance inventory and was able to replace it. The pump is custom made for my facility at a factory in Singapore and takes 8 weeks to get ordered and delivered, even expedited. What is the probability the spare I installed will survive at least until I get another spare in? d. Suppose I just installed 300 of these pumps in my plant. By what time can I expect 20% of these pumps to have failed?

Explanation / Answer

1.) Since it is a scenario of arrival/ unit of time we can use poisson distribution over here.

A/q 30000 requests are received per hour ,So Requests follow poisson with 30000/hour or Poi(25/3) per second

a.) So, for the next 10 seconds P(poi(250/3)=50=exp(-250/3)*(250/3)^50/50!=0.000023262

b.) Since the main distribution follows a poisson distribution, the waiting time distribution is the exponential distribution, So, P(WT>0.1)=P(Exp(25/3)>0.1)=1-exp(-25/3*0.1)=0.5654

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