I am trying to study probability and this is one of the unsolved exercises I encountered. Please help.
Suppose $X$ has distribution function $F$, What is distribution function of random variable $Y$ where $Y$ is defined as $Y = aX+b$
I am trying to study probability and this is one of the unsolved exercises I encountered. Please help.
Suppose $X$ has distribution function $F$, What is distribution function of random variable $Y$ where $Y$ is defined as $Y = aX+b$
HINT: Start with $ F_Y(y) = \mathbb{P}\left(Y \leqslant y\right)=\mathbb{P}\left(a X + b \leqslant y\right) $ If you manage to rewrite the latter as $\mathbb{P}\left(X \leqslant g(y) \right)$ you would establish the relationship between $F_Y(y)$ and $F_X(g(y))$.