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

X is a Poisson random variable with a rate 11 Calculate P(X = 8)?
A continuous variable Y has a probability density function for which the moment generating function is given by M(t)=e^(2*t+72*t^2). What is the variance of the variable, Var[Y]?
4. A continuous random Variable X has probability Density function defined by f(x) = 5-5x; 0<=x<=1, =0 otherwise, find the mean and the variance of the distribution.
5. Suppose the distance traveled in an ride-share trip in a certain area can be modeled by a random variable that has the probability density function f(x) = 1/5 for 5 < x < 10. For the same area, the dynamic pricing algorithm of the ride-share app charges X? – 10 dollars when X miles are traveled. (a) What is the expected distance traveled in a ride? (b) What is the expected cost of a ride? (c) What is the probability that a ride costs less than 50 dollars?
A random variable X has a PDF f(x)=C(8*x−x^2) for 0<x<8, and is equal to 0 outside this range. (a) Find the value of the constant C (b) Find the CDF of X and use it to compute the probability that X≥4 (c) Calculate the mean and variance of X
b) Universiti has conducted a survey to know the perception of the students towards online and distance learning. A mail questionnaire was distributed. The proportion of people who respond to a certain mail questionnaire is a continuous random variable X, which has the probability density function as follow; ii) i) Find the expected value of X iii) =(x + 2) f(x) = 16' Calculate the variance of X Find V (2x - 2) 0 < x < 4 elsewhere
What is Pr(X = n) for a Poisson random variable with parameter l? What is E(X ) in this case?
The daily consumption of natural gas in liters of a particular building is a random variable x with probability density function X 1≤x≤2 k(1-1/2) f(x) = - { *( 0 elsewhere a) calculates the appropriate value of K so that the distribution is probabilistic density b) calculate the expected value c) calculate the standard deviation
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
Find the variance of the random variable Y where 3 )2,0y < 2 fr(u) 8
Suppose that a positive continuous random variable X has probability density function given by f(x)=c(14-5x^2), where c is a constant. What is the variance of this random variable? TYPE YOUR ANSWER AS THE NEAREST NUMBER WITH TWO DECIMAL DIGITS.
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 ?

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