Absolutely continuous random variable X can take values only in the interval [4,9]. On this segment, the distribution density of the random variable $X$ has the form: $f (x) = C (1 + 7x^{0.5} + 8x^{0.7} + 4x^{0.9})^{1.3}$, where $C$ is a positive constant.Find: 1) the constant $C$; 2) mathematical expectation $E (X)$; 3) standard deviation $\sigma_X$; 4) the quantile of the 0.9 level of the $X$ distribution.
All points except for calculating the quantile I could.I found a quantile function:
- $Q(x) = F^{-1}(x)$
but I didn't understand how to apply it. I did not find a disassembled example anywhere and therefore turned here. Please, help
To find quantile of the 0.9 level of distribution with increasing continuous c.d.f. $F$, you need to solve the equation $F(x) = 0.9$. So, find c.d.f. and equate to $0.9$. Find $x$. It is the quantile of the 0.9 level.