The given problem illustrates a situation where the time a hospital patient must wait for a nurse's assistance is modeled by a continuous random variable with a specific density function. The function is given by:\[ f(t) = \frac{1}{3} e^{-t/3} \]for \( t \geq 0 \) (time is measured in minutes).### Questions:**(a)** What is the probability that a patient must wait for more than 4 minutes?To find this, you would calculate the probability \( P(T > 4) \).**(b)** A patient spends a week in the hospital and requests nurse assistance once each day. What is the probability that the nurse will take longer than 5 minutes to respond on (exactly) two occasions?Here, we look at a binomial distribution scenario with 7 trials (one for each day), where the probability of taking longer than 5 minutes is calculated using the given density function. We aim to find the probability of exactly two such incidents.**(c)** What is the probability that on at least one call out of seven, the nurse will take longer than 7 minutes to respond?This involves calculating the probability of the complement (nurse taking less than or equal to 7 minutes) for all seven calls and subtracting from 1 to find the probability of at least one over 7 minutes.### Explanation of the Density Function:The function \( f(t) = \frac{1}{3} e^{-t/3} \) is an exponential density function. The exponential distribution is often used to model waiting times or the time until an event occurs. Here, the rate parameter \( \lambda = \frac{1}{3} \) indicates the average rate of the event (i.e., nurse response) occurrence.

Let a random variable T denotes the waiting time for the nurse's help. Then, T~ft and ft=13e-t3…

Answered: Suppose that the amount of time a…

MATLAB: An Introduction with Applications

6th Edition

ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

Chapter1: Starting With Matlab

Section: Chapter Questions

Problem 1P

See similar textbooks

Similar questions

A probability density function of a random variable is given by f(x) = expected value, the variance, and the standard deviation. The expected value is μ≈ Round to two decimal places as needed.) 1 1 = 5+ 111 on the interval [4, 25]. Find the
Let X1, X2, ..., X„ be a random sample from a Uniform(0,0 +1) population with 0 > 0, *(4)"^( +1) be the median of the random sample. X where n is an even integer. Let M Find the probability density function of the median M. Find the expected value and variance of M.
Let S be a continuous random variable representing the students' study time (in hours) for their Statistics final paper. The probability density function is given by: = {(2 + + 5 4s 15 f(s) = i) Calculate the expected value of S. ii) Calculate the variance of S. iii) Determine E (1145 - 7S - 6S²). ,1 ≤s≤4 , otherwise
Q3/ consider a random variable X with density function 0.25(2 + 0.5x) 0.5 < x < 1.5 f (x) = elsewhere Find the variance for g(X) = 3X* +2
A continuous random variable X has probability density function fx(x) given by fx(x) = k (2-x)(x - 5), 2≤x≤5, = 0, elsewhere. Find the value of k, and hence deduce the mean and variance of X. What are the values of the mode and median of the distribution of X?
Can someone please explain it ASAP?!!!
What are the expected value and the standard deviation of the area of the circle whose radius is a random variable X with density function f(x) = 1 for 0 < x < 1 and f(x) = 0 otherwise ?
When crossing the Golden Gate Bridge traveling into San Francisco, all drivers must pay a toll. Suppose the amount of time (in minutes) drivers wait in line to pay the toll follows an exponential distribution with a probability density function of f(x) = 0.2e−0.2x. c. What is the probability that a driver spends more than 10 minutes to pay the toll? (Round intermediate calculations to at least 4 decimal places and final answer to 4 decimal places.) d. What is the probability that a driver spends between 4 and 6 minutes to pay the toll? (Round intermediate calculations to at least 4 decimal places and final answer to 4 decimal places.)
The repair time (in hours) for a certain machine is a random variable with probability density function: fx(x) = {0 if x > 0 otherwise xe a) Find the cumulative distribution function of the repair times. b) What is the probability that the repair time is less than 2 hours? c) What is the probability that the repair time is between 1.5 and 3 hours?
Suppose an electric-vehicle manufacturing company estimates that a driver who commutes 50 miles per day in a particular vehicle will require a nightly charge time of around 1 hour and 40 minutes (100 minutes) to recharge the vehicle's battery. Assume that the actual recharging time required is uniformly distributed between 85 and 115 minutes. (a) Give a mathematical expression for the probability density function of battery recharging time for this scenario. (b) What is the probability that the recharge time will be less than 108 minutes? (c) What is the probability that the recharge time required is at least 92 minutes? (d) What is the probability that the recharge time required is between 95 and 110 minutes?
Suppose random variable Y represents a random number generator that can take any value between 1 and 11. Then the density curve of the outcomes has constant height between 1 and 11, and height of 0 elsewhere. What’s the height of the density curve between 1 and 11? What is the probability that Y<2? What is the probability that Y=2? Can Y=2 happen as an event for this random number generator? What is the probability that Y=0? Can Y=0 happen as an event for this random number generator?
Suppose that the random variables X and Y have the following joint probability density function. f(x, y) = ce-8x - 5y, 0 0).

SEE MORE QUESTIONS

Recommended textbooks for you

MATLAB: An Introduction with Applications

Statistics

ISBN:

9781119256830

Author:

Amos Gilat

Publisher:

John Wiley & Sons Inc

Probability and Statistics for Engineering and th…

Statistics

ISBN:

9781305251809

Author:

Jay L. Devore

Publisher:

Cengage Learning

Statistics for The Behavioral Sciences (MindTap C…

Statistics

ISBN:

9781305504912

Author:

Frederick J Gravetter, Larry B. Wallnau

Publisher:

Cengage Learning

MATLAB: An Introduction with Applications

Statistics

ISBN:

9781119256830

Author:

Amos Gilat

Publisher:

John Wiley & Sons Inc

Probability and Statistics for Engineering and th…

Statistics

ISBN:

9781305251809

Author:

Jay L. Devore

Publisher:

Cengage Learning

Statistics for The Behavioral Sciences (MindTap C…

Statistics

ISBN:

9781305504912

Author:

Frederick J Gravetter, Larry B. Wallnau

Publisher:

Cengage Learning

Elementary Statistics: Picturing the World (7th E…

Statistics

ISBN:

9780134683416

Author:

Ron Larson, Betsy Farber

Publisher:

PEARSON

The Basic Practice of Statistics

Statistics

ISBN:

9781319042578

Author:

David S. Moore, William I. Notz, Michael A. Fligner

Publisher:

W. H. Freeman

Introduction to the Practice of Statistics

Statistics

ISBN:

9781319013387

Author:

David S. Moore, George P. McCabe, Bruce A. Craig

Publisher:

W. H. Freeman

SEE MORE TEXTBOOKS