Science:Math Exam Resources/Courses/MATH103/April 2009/Question 07 (a)
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Question 07 (a) 

Streptococcus viridans bacteria divide along a preferred axis and therefore form chains when they divide. You study a population of S. viridans in a blood culture. Let X be the length (in µm) of a randomly chosen chain. Its distribution is described by the probability density function Find the expected length of a chain (i.e. the expected value of X).

Make sure you understand the problem fully: What is the question asking you to do? Are there specific conditions or constraints that you should take note of? How will you know if your answer is correct from your work only? Can you rephrase the question in your own words in a way that makes sense to you? 
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Hint 

Use the formula for the continuous expected value. 
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Solution 

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Please rate my easiness! It's quick and helps everyone guide their studies. To find the expected lenght, we multiply the length x with the probability density function p(x) and integrate over all possible lengths. In other words, the mean, or expected value, E[X] is given by In this problem a = 1, b = e and p(x) = 1/x, thus 