Suppose small aircraft arrive at a certain airport according to a Poisson distribution with a rate of
7 per hour. Find the probability that there will be at least four arrivals in an hour
Solution
X ~ Po(7) P(X >= 4) = 1 - P(X <= 3) = 1 - poissoncdf(7, 3).
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Suppose someone claims to have gotten 4 heads in a row when she flip.pdf
1. Suppose someone claims to have gotten 4 heads in a row when she flipped a fair coin. Would
you believe her? Support your answer using probability.
Solution
let X is a Bernoulli random variable with success probability p and success is
occurance of head.my sample is 1,1,1,1. want to test p=1/2 vs p?1/2 . y= X1+X2+X3+X4 ~
Binomial(4,p).Test statistic will be y which will follow Binomial(4,1/2 ) under null .4 will fall in
the rejection region.For this sample my observed y is 4.so we will reject the null based on this
sample.We will noe believe that the coin is a fair one