4. Over 500 million tweets are sent per day. Assume that the number of tweets pe

Question

4. Over 500 million tweets are sent per day. Assume that the number of tweets per hour follows a Poisson distribution and that Bob receives on average 7 tweets during his lunch hour. a. What is the probability that Bob receives no tweets during his lunch hour? Please copy your R code and the result and paste them here. b. What is the probability that Bob receives at least 4 tweets during his lunch hour? Please copy your R code and the result and paste them here. c. What is the expected number of tweets Bob receives during the first 30 minutes of his lunch hour? What is the probability that Bob receives no tweets during the first 30 minutes of his lunch hour? Please copy your R code and the result and paste them here.

Explanation / Answer

Answer:---'

lambda = 7 tweets per hour

(A)
P(X = 0) = e^(-lambda)*lambda^x/x! = e^(-7)*7^0/0! = e^(-7) = 0.000912

(B)
P(X >= 4) = 1 - P(X <= 3)
P(X <= 3) this can be found using excel funtions
P(X <= 3) = 0.08177 (excel function: =POISSON.DIST(3,7,TRUE))

P(X >= 4) = 1 - 0.08177 = 0.9182

(C)
For 30mins expected number of tweets = 7/2 = 3.5

(D)
lambda = 3.5
P(X = 0) = e^(-lambda)*lambda^x/x! = e^(-3.5)*3.5^0/0! = e^(-3.5) = 0.030197

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