**Understanding Waiting Times at Kroger**Do you dislike waiting in line? The supermarket chain Kroger has employed computer simulation and information technology to significantly reduce the average waiting time for customers across its 2,300 stores. Utilizing a novel system called QueVision, Kroger can better predict when customers will be checking out, reducing the average waiting time to just 26 seconds.**Assumptions:**- Waiting times at Kroger are assumed to be exponentially distributed.**Questions:****a. Probability Density Functions**- Which of the following probability density functions of waiting time is applicable at Kroger?1. \( f(x) = \frac{1}{\mu} e^{\frac{x}{\mu}} = \frac{1}{26} e^{-\frac{x}{26}} \) for \( x \geq 0 \)2. \( f(x) = \frac{1}{\mu} e^{-\frac{x}{\mu}} = \frac{1}{26} e^{-\frac{x}{26}} \) for \( x \geq 0 \)3. \( f(x) = \frac{1}{\mu} e^{-\frac{x}{\mu}} = \frac{1}{26} e^{-\frac{x}{26}} \) for \( x \leq 0 \)4. \( f(x) = \frac{1}{\mu} e^{-\frac{x}{\mu}} = \frac{1}{26} e^{\frac{x}{26}} \) for \( x \geq 0 \)**b. Probability of Waiting Between 15 and 30 Seconds**- What is the probability that a customer will have to wait between 15 and 30 seconds (to 4 decimals)?**c. Probability of Waiting More Than 2 Minutes**- What is the probability that a customer will have to wait more than 2 minutes (to 4 decimals)?**Note:**- The correct solution for each part requires knowledge of exponential distributions and how to compute probabilities based on them.

Let X denote the waiting times at Kroger. Given that X follows Exponential with mean = 26 seconds.

Answered: a. Which of the probability density…

MATLAB: An Introduction with Applications

6th Edition

ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

Chapter1: Starting With Matlab

Section: Chapter Questions

Problem 1P

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2. In probability, it is common to model the deviation of a day's temperature from the monthly average temperature using the Gaussian probability density function, f(t) = This means that the probability that the day's temperature will be between t = a and t = b different from the monthly average temperature is given by the area under the graph of y = f(t) between t = a and t = b. A related function is 2 F(1) = e2/9 dt, r20. This function gives the probability that the day's temperature is between t = -x and t = r different from the monthly average temperature. For example, F(1) = (0.36 indicates that there's roughly a 36% chance that the day's temperature will be within 1 degree (between 1 degree less and 1 degree more) of the monthly average. 1 (a) Find a power series representation of F(r) (write down the power series using sigma notation). (b) Use your answer to (a) to find a series equal to the probability that the day's temperature will be within 2 degrees of the monthly average.…
Please answer number one.
How were the answers of 0.5000, 0.3090, and 0.3459 attained?
a. Find the 50-th percentile of X. That is to say the value of x such that P (X ≤ x) = 0.5. b. Now say you have two independent jet engines. What is the probability that only one of themwill last more than 12 months before needing to be rebuilt? c. Find the probability density function f(x) by taking the derivative of F(x) with respect to x.
Please only do iii. & iv.
The waiting line at a popular bakery shop can be quite long. Suppose that the waiting time in minutes has probability density function f(x) = 0.2-e 02x. Determine the following: (a) F(x). O F(x) = 10.2.x -0.2.x O F(x) = 1 + e-02 O F(x) = 1-e-0.2-x F(x) = 1 + e02-x (b) Probability that a customer waits more than 22 minutes: Round your answer to three decimal places (e.g. 0.987). P = i (c) Probability that a customer waits less than 8 minutes: Round your answer to three decimal places (e.g. 0.987). P = i
Find the required probabilities using the exponential density function e-n, [0, c0). f(t) = The waiting time t (in minutes) for service at the checkout at a grocery store is exponentially distributed with A = 2. Find the probabilities of waiting less than 3 minutes, more than 3 minutes but less than 5 minutes, and at least 3 minutes. (Round your answers to three decimal places.) (a) less than 3 minutes (b) more than 3 minutes but less than 5 minutes (c) at least 3 minutes
2.5.8The random variable X measures the concentration of ethanol in a chemical solution, and the random variable Ymeasures the acidity of the solution. They have a joint probability density function f(x, y) = A(20-x-2y) for 0 ≤ x ≤ 5 and 0 ≤ y = 5, and f(x, y) = 0 elsewhere. (a) What is the value of A? (b) What is P(1 ≤ X≤ 2, 2 ≤ Y≤ 3)? (c) Construct the marginal probability density functions f(x) and fy(y). (d) Are the ethanol concentration and the acidity independent? (e) What are the expectation and the variance of the ethanol concentration? (f) What are the expectation and the variance of the acidity? (g) If the ethanol concentration is 3, what is the conditional probability density function of the acidity? (h) What is the covariance between the ethanol concentration and the acidity? (1) What is the correlation between the ethanol concentration and the acidity?
Q. 6 Find 30th percentile, median and 70th percentile for the following probability density functions: X < 0 0s X < 1 0s X s 1.3 1.3 (i) fx(x) = 3x2 1s Xs 2 (ii) fx(x) = %3D %3D 2-x 1.3 < X s 2 14 otherwise 0.7 otherwise
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The Exponential pdf for continuous random variable Y takes the form e-ylß y > 0 f(V) = for ß > 0. y 1.6) Give your answer to three decimal places.
2. In probability, it is common to model the deviation of a day's temperature from the monthly average temperature using the Gaussian probability density function, 1.-/9 f(t) = V9T This means that the probability that the day's temperature will be between t = a and t = b different from the monthly average temperature is given by the area under the graph of y = f(t) between t a andt = b. A related function is %3D F(x) = -2/9 dt, 2 0. %3D V9n Jo This function gives the probability that the day's temperature is between t = -x and t = x different from the monthly average temperature. For example, F(1) 0.36 indicates that there's roughly a 36% chance that the day's temperature will be within 1 degree (between 1 degree less and 1 degree more) of the monthly average. 1 (a) Find a power series representation of F(x) (write down the power series using sigma notation). (b) Use your answer to (a) to find a series equal to the probability that the day's temperature will be within 2 degrees of the…

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