Science:Math Exam Resources/Courses/MATH103/April 2015/Question 07 (a)
• Q1 (a) (i) • Q1 (a) (ii) • Q1 (a) (iii) • Q1 (b) (i) • Q1 (b) (ii) • Q1 (b) (iii) • Q1 (c) (i) • Q1 (c) (ii) • Q1 (c) (iii) • Q1 (d) (i) • Q1 (d) (ii) • Q1 (e) (i) • Q1 (e) (ii) • Q1 (e) (iii) • Q2 (a) • Q2 (b) • Q2 (c) • Q2 (d) • Q2 (e) • Q3 (a) • Q3 (b) • Q3 (c) • Q4 • Q5 (a) • Q5 (b) • Q5 (c) • Q6 (a) • Q6 (b) • Q6 (c) • Q7 (a) • Q7 (b) • Q7 (c) • Q7 (d) • Q8 • Q9 • Q10 (a) • Q10 (b) •
Question 07 (a) 

Consider the Normal (or Gaussian) probability density function (pdf ) given by for . (a) Find the mean . 
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? 
If you are stuck, check the hint below. Consider it for a while. Does it give you a new idea on how to approach the problem? If so, try it! 
Hint 

When a probability density function is given, the formula for the mean value is

Checking a solution serves two purposes: helping you if, after having used the hint, you still are stuck on the problem; or if you have solved the problem and would like to check your work.

Solution 

Found a typo? Is this solution unclear? Let us know here.
Please rate my easiness! It's quick and helps everyone guide their studies. Using the Hint, the mean is The last inequality follows from the parity of the integrand. Indeed, is odd and is even, so that the integrand is an odd function. The answer: . 