Continuous Random Variables including exponential distribution

Question

Let $X$ be an exponential random variable with parameter $\lambda=9$. Let $Y$ be the random variable defined by $Y=10e^X$. Compute the probability density function of $Y$: what is $f_Y(t)$ (for $t\geq10)$?

Answer 1

Here are some hints to get you started.

The cdf of $Y$ is given by

$$\begin{align*} F_Y(t) &=P(Y\leq t)\\\\ &=P(10e^X \leq t) \end{align*}$$

Can you go from here to get this in terms of the cdf of $X$? That is, $P(X\leq x)$.