Here are the historical probabilities p(x) = P(X = x) that a fixed length of cast-iron piping will be manufactured and be found, on inspection, to have various numbers X of potentially weakening defects:x 0 1 2 3 4p(x) .45 .21 .13 .12 ,09F(x)Calculate the expected number of defects in a pipe E(X).
Mathematics · College · Tue Nov 03 2020
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To calculate the expected number of defects in a pipe E(X), also known as the mean of the probability distribution, you can use the following formula:
E(X) = Σ [x * p(x)]
where x is the value of the random variable and p(x) is the probability of x occurring. Using the given probabilities:
E(X) = (0 * 0.45) + (1 * 0.21) + (2 * 0.13) + (3 * 0.12) + (4 * 0.09)
= 0 + 0.21 + 0.26 + 0.36 + 0.36
= 1.19
So, the expected number of defects in a pipe E(X) is 1.19.