6. Probability: A nonnegative function $f$ is called a probability density function if| \int_{-\infty}^{\infty} f(t) d t=1 The probability that $x$ lies between $a$ and $b$ is given by P(a \leq x \leq b)=\int_{a}^{b} f(t) dt And the expected value of $x$ is given by E(x)=\int_{-\infty}^{\infty) t f(t) dt If the average time it takes for UMD parking enforcement to issue a ticket after your meter expires is given by the exponential distribution $f(t)=\left\ {\begin{array}{cc)0 & \text { if } to 0.125 e^{-0.125 t} & \text { if } t \geq O\end{array} ight. $ where $t$ is minutes after the meter expires. A. Show that $f$ satisfies the first condition for a probability density function. B. Determine the probability that you have a ticket if you get to your car 10 minutes after time runs out on your meter. C. Determine the expected (average) amount of time it takes to get a ticket. SP.SS. 380