Question

Suppose that only 0.1 of all computers of a certain type experience cpu failure during the warranty period. Consider a sample of 7000 computers. (a) what are the expected value and standard deviation of the number of computers in the sample that have the defect?

Answer 1

a.) E(X) of a poisson distribution is λ λ which is np which is (10,000)(.001)=10. V(X) is also λ λ or 10. The standard deviation is the squareroot of V(X) or sqrt(10)? b.) To do this, would I take the sum of the probability of 10 machines having a failure to infinity cpus failing? (i.e. p(10;10) + p(11;10) + ... p(inf,10)) p ( x ≥ 10 ; 10 ) = ∞ ∑ x = 10 e − 10 10 x x ! p(x≥10;10)=∑x=10∞e−1010xx! c.) To find this, would I use p(0;10)? If so: p ( 0 ; 10 ) = e − 10 10 0 0 ! p(0;10)=e−101000! p ( 0 ; 10 ) = e − 10 ( 1 ) 1 = e − 10