- #1
Saracen Rue
- 150
- 10
Homework Statement
A probability density function is defined by ##f\left(x\right)=\left|a\right|\left(x+1\right)-\left(ax-1\right)^2## where ##x∈[0,b]##. Determine the values of the constants ##a## and ##b##, given that the graph passes through the point ##(b,0)##.
Homework Equations
##∫_a^bf(x)dx=1## where ##f(x)## is a probability density function
The Attempt at a Solution
Okay, so I know I'm attempting to solve ##∫_0^bf(x)dx=1## for ##b##, but I'm rather unsure of how to do that in this instance due to ##a## being a second unknown variable.
I've attempted finding the x-intercept, ##b## of ##f(x)## but it is dependent on the variable ##a##. I then tried to find ##a## in terms of x and use that to somehow find ##b## but I soon realized that wasn't going anywhere. Normally for these types of questions, ##a## would just be a dilation factor, meaning it doesn't effect the values of the x-intercepts and can just be taken out as a common factor before integrating. I'm not sure why I'm supposed to do when it effects the location of the x-intercepts.