- #1
Linder88
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Homework Statement
If you already have waited five minutes at the bus stop, what is the probability of having to wait additionally five minutes or more?
Homework Equations
Declare a random time T, together with the CDF shown below, which specify the time (in minutes) that a frozen traveller has to wait at the bus stop before the bus arrives
\begin{equation}
F_T(t)=
\begin{cases}
\bigg (\frac{t}{2}\bigg ]^2,0\leq t\leq 1\\
\frac{t}{4},1\leq t\leq 2\\
\frac{1}{2},2\leq t \leq 10\\
\frac{t}{20},10\leq t\leq 20\\
1,t\geq 20
\end{cases}
\end{equation}
The Attempt at a Solution
We are looking for $P[T\geq 5|T>5]$
\begin{equation}
P[T\geq 5|T>5]\frac{P[T\geq 5,T\geq 5]}{p[T=5]}=\frac{P[T\geq 5]P[T>5]}{P[T=5]}=\frac{1}{2}
\end{equation}