Exam P Practice Problem 107 – wait time at a busy restaurant

Both 107-A and 107-B use the following probability density function.

    \displaystyle  f(x) = \left\{ \begin{array}{ll}                   \displaystyle  \frac{1}{450} \ (30-x) &\ \ \ \ \ \ 0 < x < 30 \\           \text{ } & \text{ } \\          \displaystyle  0 &\ \ \ \ \ \ \text{otherwise} \\                              \end{array} \right.

Problem 107-A

The wait time (in minutes) for a table at a busy restaurant on the weekend is distributed according to the density function f(x) given above.

A customer plans to dine in this restaurant on two different weekends.

Determine the expected value of the longest wait of these two visits to the restaurant.

      \displaystyle \bold ( \bold A \bold ) \ \ \ \ \ \ \ \ \ \ \ \  \bold 1 \bold 0 \bold . \bold 0

      \displaystyle \bold ( \bold B \bold ) \ \ \ \ \ \ \ \ \ \ \ \ \bold 1 \bold 1 \bold . \bold 0

      \displaystyle \bold ( \bold C \bold ) \ \ \ \ \ \ \ \ \ \ \ \ \bold 1 \bold 2 \bold . \bold 8

      \displaystyle \bold ( \bold D \bold ) \ \ \ \ \ \ \ \ \ \ \ \ \bold 1 \bold 3 \bold . \bold 5

      \displaystyle \bold ( \bold E \bold ) \ \ \ \ \ \ \ \ \ \ \ \ \bold 1 \bold 4 \bold . \bold 0

\text{ }

\text{ }

\text{ }

\text{ }

Problem 107-B

The wait time (in minutes) for a table at a busy restaurant on the weekend is distributed according to the density function f(x) given above.

A customer plans to dine in this restaurant on two different weekends.

Determine the expected value of the shortest wait of these two visits to the restaurant.

      \displaystyle \bold ( \bold A \bold ) \ \ \ \ \ \ \ \ \ \ \ \  \bold 4 \bold . \bold 5

      \displaystyle \bold ( \bold B \bold ) \ \ \ \ \ \ \ \ \ \ \ \ \bold 6 \bold . \bold 0

      \displaystyle \bold ( \bold C \bold ) \ \ \ \ \ \ \ \ \ \ \ \ \bold 7 \bold . \bold 0

      \displaystyle \bold ( \bold D \bold ) \ \ \ \ \ \ \ \ \ \ \ \ \bold 8 \bold . \bold 6

      \displaystyle \bold ( \bold E \bold ) \ \ \ \ \ \ \ \ \ \ \ \ \bold 1 \bold 0 \bold . \bold 0

\text{ }

\text{ }

\text{ }

\text{ }

\text{ }

\text{ }

\text{ }

\text{ }

Answers

probability exam P

actuarial exam

math

Daniel Ma

mathematics

dan ma actuarial science

daniel ma actuarial science

Daniel Ma actuarial

dan ma statistical actuarial

daniel ma statistical actuarial

\copyright 2019 – Dan Ma

Advertisements

Leave a Reply

Fill in your details below or click an icon to log in:

WordPress.com Logo

You are commenting using your WordPress.com account. Log Out /  Change )

Google photo

You are commenting using your Google account. Log Out /  Change )

Twitter picture

You are commenting using your Twitter account. Log Out /  Change )

Facebook photo

You are commenting using your Facebook account. Log Out /  Change )

Connecting to %s

%d bloggers like this: