Let X be an exponential random variable with probability density function: {} 0 f(x) = Ae-...
Fantastic news! We've Found the answer you've been seeking!
Question:
Transcribed Image Text:
Let X be an exponential random variable with probability density function: {} 0 f(x) = Ae-² 120 x<0 (a) Let Y= (X-1)2. Find the probability density function of Y. (b) Find the moment generating function of X. (e) Calculate the mean and variance of X. (d) Suppose the time to build a house is described by an exponential distribution with parameter A (=2 years). Suppose the cost per year is €100,000 with a fixed design cost of €50.000. i) What is the average cost required to build a house? ii) What is the variance of the cost required to build a house? iii) What is the probability that a minimum of €200,000 is required? Let X be an exponential random variable with probability density function: {} 0 f(x) = Ae-² 120 x<0 (a) Let Y= (X-1)2. Find the probability density function of Y. (b) Find the moment generating function of X. (e) Calculate the mean and variance of X. (d) Suppose the time to build a house is described by an exponential distribution with parameter A (=2 years). Suppose the cost per year is €100,000 with a fixed design cost of €50.000. i) What is the average cost required to build a house? ii) What is the variance of the cost required to build a house? iii) What is the probability that a minimum of €200,000 is required?
Expert Answer:
Answer rating: 100% (QA)
a Given the probability density function of random variable X fxAeAz where A is a distribution param... View the full answer
Related Book For
Applied Statistics And Probability For Engineers
ISBN: 9781118539712
6th Edition
Authors: Douglas C. Montgomery, George C. Runger
Posted Date:
Students also viewed these mathematics questions
-
Let X be an Exponential random variable with E(X) = 1/. Define Y = [X], i.e., Y is the least integer that is greater than or equal to Y. For instance, if X = 5.3, then Y = 6. If X = 4.99, then Y = 5....
-
Let x be an exponential random variable with l = 0.5. Calculate the following probabilities: a. P (x < 5) b. P (x > 6) c. P (5 x 6) d. P (x 2) e. The probability that x is at most 6
-
The standard deviation for a random variable with probability density function f and mean μ is defined by Find the standard deviation for an exponential density function with mean μ. 1/2...
-
Make a Marketing Plan for business during the Covid 19 Pandemic as it is today. Position yourself as an entrepreneur looking to open a new business or expand your existing business. Use assumptions...
-
Dimitry Chernitsky is seeking part-time employment while he attends school. He is considering purchasing technical equipment that will enable him to start a small training services company that will...
-
Identify types of data.
-
True or False: If \(P W>0\), then \(I R R>M A R R\).
-
The Balcar Companys auditors are developing an audit plan to review the companys systems development procedures. Their audit objectives are to ensure that 1. The system was judged necessary and...
-
Is discord supported by a relational database, hierarchical database, NoSQL database, or something else?Explain
-
There is a database that contains a website's traffic data over a period of 30 days. The first table contains users' information including the user type (user, crawler, admin). The second table...
-
You are provided with some sample code for searching/sorting algorithms, which are currently based on integer arrays. However, you are tasked to utilize a custom class that will implement comparable...
-
1. Cost of goods sold included: Attempted: 0/1 Attempted: 0/1 Moolan Enterprise, owned by Moolan, is in the business of trading in beauty equipment, with an accounting year end of 31 December. Most...
-
Statement of Comprehensive Income for the year ended 31 December 2022 Sales (all credit) Cost of sales Opening inventory Purchases (all credit) Closing inventory Gross profit Statement of Financial...
-
(1) Life on a medieval estate centered on the castle, the residence of the lords family and refuge for the estates population in time of war. (2) After Christian crusaders had studied Byzantine and...
-
Explain why empowerment is so important to supervisors, employees, and organizations, individually and as a whole. Please share/provide some firsthand examples from your work or social experiences....
-
1) Explain why the war in Ukraine was expected to drive food prices up. Use a graph or graphs to support your answer. 2) In addition to the war, what other factors were expected to contribute to an...
-
In May 2016, Mark Hopkins, managing director of Tel-Comm-Tek (TCT) India, a subsidiary of a U.S. MNE, announced his retirement. During his tenure, Hopkins had overseen the rising growth, market...
-
The executor of Gina Purcells estate has recorded the following information: Assets discovered at death (at fair value): Cash . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ....
-
Define X as the number of under filled bottles from a filling operation in a carton of 24 bottles. Sixty cartons are inspected and the following observations on X are recorded: Values 0 1 2 3...
-
A group of civil engineering students has tabulated the number of cars passing eastbound through the intersection of Mill and University Avenues. They obtained the data in the following table. (a)...
-
You have fit a regression model with two regressors to a data set that has 20 observations. The total sum of squares is 1000 and the model sum of squares is 750. (a) What is the value of R 2 for this...
-
Let \(\left\{x_{n}ight\}_{n=1}^{\infty}\) be a sequence of real numbers defined by \[x_{n}=\left\{\begin{array}{rl}-1 & n=1+3(k-1), k \in \mathbb{N} \\0 & n=2+3(k-1), k \in \mathbb{N} \\1 &...
-
Let \(\left\{x_{n}ight\}_{n=1}^{\infty}\) be a sequence of real numbers defined by \[x_{n}=\frac{n}{n+1}-\frac{n+1}{n},\] for all \(n \in \mathbb{N}\). Compute \[\liminf _{n ightarrow \infty}...
-
Each of the sequences given below converges to zero. Specify the smallest value of \(n_{\varepsilon}\) so that \(\left|x_{n}ight| n_{\varepsilon}\) as a function of \(\varepsilon\). a....
Study smarter with the SolutionInn App