- #1
Saracen Rue
- 150
- 10
Homework Statement
Presume the relation ##\frac{x}{x+y^2}-y=x## is defined over the domain ##[0,1]##.
(a) Rearrange this relation for ##y## and define it as a function, ##f(x)##.
(b) Function ##f(x)## is dilated by a factor of ##a## from the y-axis, transforming it into a probability density function, ##p(x)##. Find the value of ##a## correct to 4 decimal places.
(c) Determine the following correct to 3 decimal places:
I) The mean of ##p(x)##
II) The standard deviation of ##p(x)##
III) The median, ##m##, of ##p(x)##
(d) Calculate the probability of discrete random variable ##x## being within ##a## standard deviations either side of the mean.II) The standard deviation of ##p(x)##
III) The median, ##m##, of ##p(x)##
Homework Equations
Knowledge of integration, probability density functions, and the rearranging and solving of equations.
The Attempt at a Solution
Starting with part ##(a)##, I attempted to rearrange ##\frac{x}{x+y^2}-y=x## for ##y##. I managed to express the equation in the form ##y^3+xy^2+xy+x^2-x=0## however this is where I become stuck. I'm unsure of how to factorise this equation for ##y## and my calculator simply returns an error message when I try and use it. Is there another way to do this that I'm missing or don't know about?
Thank you for taking your time to read this :)