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The length of human pregnancies from conception to birth varies according to a distribution that is approximately Normal with mean 266266 days and standard deviation 1616 days. Choose two pregnancies independently and at random.\newline(a) What is the expected difference in the lengths of the two pregnancies?

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Q. The length of human pregnancies from conception to birth varies according to a distribution that is approximately Normal with mean 266266 days and standard deviation 1616 days. Choose two pregnancies independently and at random.\newline(a) What is the expected difference in the lengths of the two pregnancies?
  1. Expected Difference Calculation: The expected difference in the lengths of two independent random variables is the same as the expected value of the difference of those two variables. Since we are dealing with the same distribution for both pregnancies, the expected value of the difference is 00 because the mean of the differences between two identical distributions is 00.
  2. Mean of Identical Distributions: To elaborate, if XX and YY are two independent random variables with the same distribution, then E(X−Y)=E(X)−E(Y)E(X - Y) = E(X) - E(Y). Since XX and YY have the same mean, E(X)=E(Y)E(X) = E(Y), and therefore E(X−Y)=E(X)−E(X)=0E(X - Y) = E(X) - E(X) = 0.

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