How can we calculate the probability of quadratic polynomial such that
\begin{align} \ Y=a_0+a_1x+a_2x^2\\ \mathsf P\left(Y\lt y\right)=P \end{align}
with y is such a number from this polynomial and is given
thanks in advance
How can we calculate the probability of quadratic polynomial such that
\begin{align} \ Y=a_0+a_1x+a_2x^2\\ \mathsf P\left(Y\lt y\right)=P \end{align}
with y is such a number from this polynomial and is given
thanks in advance
$$P(Y<y)=\int_{a_0+a_1x+a_2x^2<y}\text{pdf}(x)\,dx=\sum_k\left.\text{cdf}(x)\right|_{l_k}^{u_k}$$ where the sum is over the (zero, one or two, possibly infinte) intervals $l_k<x<u_k$ where the quadratic inequality holds.