A software company has experienced an increase in programming errors. Four pages

Question

A software company has experienced an increase in programming errors. Four pages are randomly selected. The following table, based on prior process knowledge, describes the distribution of programming errors in the sample:

yi: 0 1 2 3 4
p(yi): 0.52 0.24 0.12 0.09 0.03

Find the probability that no programming errors are found in that sample, the probability that more than two programming errors are found in the sample, and the mean, variance, and standard deviation for the programming errors in the sample.

Explanation / Answer

Find the probability that no programming errors are found in that sample

P(X=0)=0.52

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the probability that more than two programming errors are found in the sample

P(X>2) =P(X=3) + P(X=4) =0.09 + 0.03 =0.12

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the mean, variance, and standard deviation for the programming errors in the sample.

mean= E(X) = 0.52*0 + 0.24*1 + 0.12*2 + 0.09*3 + 0.03*4 = 0.87

E(X^2) =0.52*0 + 0.24*1 + 0.12*2^2 + 0.09*3^2 + 0.03*4^2 =2.01

Var(X) = E(X^2) - [E(X)]^2 = 2.01 -0.87^2 =1.2531

standard deviation = 1.2531 =1.119419

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