2 6. Show that a gamma distribution with a > 1 has a relative maximum atx = (a- 1)ß. What happens when 0 < a < 1 and a = 1?%3D

Relative maximum =? For a gamma distribution for alpha>1

Answered: 6. Show that a gamma distribution with…

College Algebra

1st Edition

ISBN:9781938168383

Author:Jay Abramson

Publisher:Jay Abramson

Chapter6: Exponential And Logarithmic Functions

Section6.8: Fitting Exponential Models To Data

Problem 5SE: What does the y -intercept on the graph of a logistic equation correspond to for a population...

See similar textbooks

Similar questions

Olympic Pole Vault The graph in Figure 7 indicates that in recent years the winning Olympic men’s pole vault height has fallen below the value predicted by the regression line in Example 2. This might have occurred because when the pole vault was a new event there was much room for improvement in vaulters’ performances, whereas now even the best training can produce only incremental advances. Let’s see whether concentrating on more recent results gives a better predictor of future records. (a) Use the data in Table 2 (page 176) to complete the table of winning pole vault heights shown in the margin. (Note that we are using x=0 to correspond to the year 1972, where this restricted data set begins.) (b) Find the regression line for the data in part ‚(a). (c) Plot the data and the regression line on the same axes. Does the regression line seem to provide a good model for the data? (d) What does the regression line predict as the winning pole vault height for the 2012 Olympics? Compare this predicted value to the actual 2012 winning height of 5.97 m, as described on page 177. Has this new regression line provided a better prediction than the line in Example 2?
4. In the study of human metabolism, it is known that daily calorie intake of a person age 25 above primarily affects the variability in weight gain. Scientists conducted an experiment to come up with a working formula of how much will be the average weight y (in kgs.) of a person age 25 if the person regularly has x calories of daily net calorie intake. It was shown that, on the average, y is related to x by the following relationship Y = In [x+ sin² (7)] + 50, x > 1. It was also observed that the each year the average weight of a person age 25 changes at a rate 1.5 kgs. per year. How fast is the average daily net calorie intake of a person changing when the person has 4 calories of daily net calorie intake?
In a certain city, the daily consumption of electricpower in millions of kilowatt-hours can be treated as arandom variable having a gamma distribution with α = 3and β = 2. If the power plant of this city has a daily capacity of 12 million kilowatt-hours, what is the prob-ability that this power supply will be inadequate on any given day?
The variation of Y around its mean can be decomposed into which two parts?
Please solve it perfectly
A correlation of r = .85 is found between weekly sales of firewood and coughdrops over a 1-year period. Which of the following is true? (a) There is a pretty strong positive linear relationship between sales of firewood and cough drops. (b) Fire must be the cause of coughing. (c) Temperature is a possible lurking variable that is “behind” this relationship. (d) Both (a) and (c) are true. (e) None of the above.
3
5. Oxygen demand is a term blologists use to describe the axygen needed by fish and other aquatic organisms for survval. The Environmental Protection Agency conducted a study of a wetland area in Marin County, Californla. In this wetland environment, the mean oxygen demand was u=9.9 mg/L, and a= 1.7 mg/L. (Reference: EPA Report 832-R- 93- 005). Let x be a random varlable that represents oxygen demand in this wetland environment. Assume x has a probability distribution that is approximately normal. a. An oxygen demand below 8 mg/L Indicates that some organisms In the wetland environment may be dying. What is the probability that the oxygen demand will fall below 8 mg/L? b. A high oxygen demand can also indicate trouble. An oxygen demand above 12 mg/L may indicate an overabundance of organisms that endanger some types of plant life. What is the probability that the oxygen demand will exceed 12 mg/L?
Suppose that X and Y are unknowns with E(X) = 10, Var (X) = 4, E(Y)=12 and Var (Y) = 100. In addition, suppose that the correlation coefficient of X and Y is .6. Then what is the variance of X-Y?
Imagine that there is a correlation of r = 0.65 between variable X and variable Y. Based on the correlation between these two variables (and only these two variables), what is a person's predicted value on variable Y, when his X value on variable X is a z score of 1.5? Please provide your answer as a z score with a minimum of three decimal places.
What is indicated by a Pearson correlation of r = +1.00 between Xand Y? Each time X increases, there is a perfectly predictable increase in Y Every change in X causes a change in Y All of the other 3 choices occur with a correlation of +1.00. Every increase in X causes an increase in Y
18. Because ethanol contains less energy than gasoline, a researcher wants to determine if the mileage of a car (y) is affected by the percent ethanol in the gasoline (x). The true population regression line relating the mean mileage y for a given ethanol content x (in percent) is μy|x = β0 + β1x. In a controlled environment, the mileage of a car is recorded when refueled 7 times using between 0% and 10% ethanol. The least squares regression line was found to be yˆ = βˆ0 + βˆ1x = 32.96 − 0.250x. We wish to test H0 : β1 = 0 versus Ha : β1 < 0 at the α = 0.05 significance level (i.e. we want to determine if the addition of ethanol significantly decreases mean gas mileage). What is the p−value for this test? What is your conclusion? Note: s?e(βˆ1) = 0.0485. Which of the following is/are true? (A) In reference to question (18), it would be appropriate to approximate the mean mileage when the car is using 85% ethanol (B) In reference to question (18), a 95% confidence interval for β1…

SEE MORE QUESTIONS

Recommended textbooks for you

College Algebra

Algebra

ISBN:

9781938168383

Author:

Jay Abramson

Publisher:

OpenStax

College Algebra

Algebra

ISBN:

9781305115545

Author:

James Stewart, Lothar Redlin, Saleem Watson

Publisher:

Cengage Learning

Glencoe Algebra 1, Student Edition, 9780079039897…

Algebra

ISBN:

9780079039897

Author:

Carter

Publisher:

McGraw Hill

College Algebra

Algebra

ISBN:

9781938168383

Author:

Jay Abramson

Publisher:

OpenStax

College Algebra

Algebra

ISBN:

9781305115545

Author:

James Stewart, Lothar Redlin, Saleem Watson

Publisher:

Cengage Learning

Glencoe Algebra 1, Student Edition, 9780079039897…

Algebra

ISBN:

9780079039897

Author:

Carter

Publisher:

McGraw Hill

Algebra and Trigonometry (MindTap Course List)

Algebra

ISBN:

9781305071742

Author:

James Stewart, Lothar Redlin, Saleem Watson

Publisher:

Cengage Learning

Algebra & Trigonometry with Analytic Geometry

Algebra

ISBN:

9781133382119

Author:

Swokowski

Publisher:

Cengage

Linear Algebra: A Modern Introduction

Algebra

ISBN:

9781285463247

Author:

David Poole

Publisher:

Cengage Learning

SEE MORE TEXTBOOKS

6. Show that a gamma distribution with a > 1 has a relative maximum at x = (a- 1)ß. What happens when 0 < a < 1 and a = 1?