Question

The function f(t)=5/3e^(-5t/3) models a continuous probability for 0 12 years ago

Answer 1

\[0 \le t < \infty \]

Answer 2

Notice that
\[
\int_0^x \frac{5}{3}
e^{-\frac{5 t}{3}} \,
dt=1-e^{-\frac{5 x}{3}}
\]
Find x so that
\[
1-e^{-\frac{5 x}{3}}=\frac 1 2
\]
and you are done

Answer 3

\[
1-e^{-\frac{5 x}{3}}=\frac 1 2\\
e^{-\frac{5 x}{3}}=\frac 1 2\\
-\frac{5 x}{3}=-\ln (2)\\
x=\frac{3 \ln(2) }
{5}

\]

Answer 4

Interesting, the median for a discrete function and for a continuous function don't seem to correlate much at all.