For each of the following, give the name of the distribution, the values of any

Question

For each of the following, give the name of the distribution, the values of any parameters, a formula for the exact probability, and only if appropriate (a binomial distribution with large n and p close to 0 or 1), use the Poisson distribution to estimate the probability. On average, an idea comes to Dr. Einstein every 7.5 minutes. What is the probability that she has X ideas in 30 minutes? Each time a webpage is loaded, one of these twenty problems is chosen at random. If the webpage is loaded 20 times, what is the probability this problem will not be loaded? An observatory detects a very high energy cosmic ray once every thirty days, on average. What is the probability that the observatory will detect exactly two particles in thirty days?

Explanation / Answer

1.

Hence, he will have, on average, 30/7.5 = 4 ideas in 30 minutes.

Hence, we use the Poisson distribution with mean u = 4. As

Note that the probability of x successes is                      

P(x) = u^x e^(-u) / x!          

Hence, for u = 4,

P(x) = 4^x e^(-4) / x!       [ANSWER]

  

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