What are the mean and standard deviation of the probability density function given by #p(x)=kabs(x-9) # for # x in [0,18]#, with k being a constant such that the cumulative density is equal to 1?
First Normalize the distribution to 1, by integrating (compute the area) over [0, 18]
Now you can easily see the integral the area of the two triangles on [0, 18]. Thus the integral is equal to:
so the Probability distribution function: