💬 👋 We’re always here. Join our Discord to connect with other students 24/7, any time, night or day.Join Here!

$REM$ sleep is the phase of sleep when most active dreaming occurs. In a study, the amount of $REM$ sleep during the first four hours of sleep was described by a random variable $T$ with probability density function$$f(t) = \left\{ \begin{array}{ll} \frac{1}{1600} t & \mbox{if  0 \le t \le 40 }\\ \frac{1}{20} - \frac{1}{1600} t & \mbox{if  40 < t \le 80  }\\ 0 & \mbox{otherwise} \end{array} \right.$$where $t$ is measured in minutes.(a) What is the probability that the amount of $REM$ sleep is between 30 and 60 minutes?(b) Find the mean amount of $REM$ sleep

A. $\approx 59.4 \%$B. 40 $\mathrm{min}$

Discussion

You must be signed in to discuss.
Catherine R.

Missouri State University

Heather Z.

Oregon State University

Kayleah T.

Harvey Mudd College

Michael J.

Idaho State University

Lectures

Join Bootcamp

Video Transcript

Montclair State University
Catherine R.

Missouri State University

Heather Z.

Oregon State University

Kayleah T.

Harvey Mudd College

Michael J.

Idaho State University

Lectures

Join Bootcamp