- #1
Saracen Rue
- 150
- 10
Homework Statement
A probability density function, ##p\left(x\right)=\int _{-a}^a\left(f\left(x,\left(a-y\right)\right)-f\left(y,ax\right)\right)dy##, can be formed from the bivariate function ##f\left(x,y\right)=y\sqrt{\left(x-2\right)^2-y}## over the domain ##[0,b]## - where ##b## is the coordinate of the x-intercept.
(a) Determine the values of ##a## and ##b## correct to 5 decimal places
(b) Calculate the expected value, variance and standard deviation of ##p(x)## correct to 4 decimal places
(c) Find the percentage probability of the continuous random variable ##X## being withing ##|a|## standard deviations either side of the mean
(b) Calculate the expected value, variance and standard deviation of ##p(x)## correct to 4 decimal places
(c) Find the percentage probability of the continuous random variable ##X## being withing ##|a|## standard deviations either side of the mean
Homework Equations
Knowledge or probability density functions, including integral applications.
The Attempt at a Solution
Well I know that I need to substitute the actual values for ##f\left(x,\left(a-y\right)\right)## and ##f\left(y,ax\right)## into ##p(x)## to be able to integrate ##\int _{-a}^a\left(f\left(x,\left(a-y\right)\right)-f\left(y,ax\right)\right)dy##, and then I'd need to solve ##int_0^b p(x)dx for b and then use that to solve for a. However, when I attempt to do this on my calculator I receive and error message. Does anyone know how I could do this?