
A First Course in Probability (10th Edition)
10th Edition
ISBN: 9780134753119
Author: Sheldon Ross
Publisher: PEARSON
expand_more
expand_more
format_list_bulleted
Question
PLEASE DO PART D ONLY. I HAVE SOLVED THE REST, I JUST CAN'T SOLVE PART D.
beta 1 is a non random constant.
Please solve d part explain step by step
![Let X₁, t = 0, ±1, ±2, · · · and Yt, t = 0, ±1, ±2, . be two independent time series with means
0 and autocovariance r₁(h) and r2(h), respectively. That is
Cov[Xt, Xt+h] = r₁(h),
Cov[Yt, Yt+h] = r₂(h) and cov[Xt, Ys] = 0
r₁(0)] and Var[Yt]
for all t,s,h, (in particular, Var [X₁
r2(0)). Consider the time series
Zt = BoXtYt-2 +5Xo, t = 0±1,±2,..., where ßo and ß₁ are nonrandom constants.
=
=
(a) Find the mean and variance of Zt.
(b) Find the autocovariance function of the time series {Zt, t = 0±1, ±2, · · · }.
(c) Is {Zt,t=0±1, ±2, · · · }. stationary?
(d) Let Z, be: 1.6, 28.1, 7.8, 4.0, 9.6, 0.2, 18.7, 16.5, 4.6, 9.3, 3.5, 0.1, 11.5, 0.0, 9.3, 5.5, 70.2, 0.7,
38.6, 11.3, 3.3, 8.9, 11.1, 64.3, 16.6, 7.3, 3.2, 23.9, 0.6.
Find the estimate of the trend Î; using ordinary linear least square method.](https://content.bartleby.com/qna-images/question/34b44b37-e66b-4c48-a846-aeedd1db2b78/d8e2da5d-907f-4fb4-b944-7d361d0399dd/0dh72hr_thumbnail.png)
Transcribed Image Text:Let X₁, t = 0, ±1, ±2, · · · and Yt, t = 0, ±1, ±2, . be two independent time series with means
0 and autocovariance r₁(h) and r2(h), respectively. That is
Cov[Xt, Xt+h] = r₁(h),
Cov[Yt, Yt+h] = r₂(h) and cov[Xt, Ys] = 0
r₁(0)] and Var[Yt]
for all t,s,h, (in particular, Var [X₁
r2(0)). Consider the time series
Zt = BoXtYt-2 +5Xo, t = 0±1,±2,..., where ßo and ß₁ are nonrandom constants.
=
=
(a) Find the mean and variance of Zt.
(b) Find the autocovariance function of the time series {Zt, t = 0±1, ±2, · · · }.
(c) Is {Zt,t=0±1, ±2, · · · }. stationary?
(d) Let Z, be: 1.6, 28.1, 7.8, 4.0, 9.6, 0.2, 18.7, 16.5, 4.6, 9.3, 3.5, 0.1, 11.5, 0.0, 9.3, 5.5, 70.2, 0.7,
38.6, 11.3, 3.3, 8.9, 11.1, 64.3, 16.6, 7.3, 3.2, 23.9, 0.6.
Find the estimate of the trend Î; using ordinary linear least square method.
Expert Solution

This question has been solved!
Explore an expertly crafted, step-by-step solution for a thorough understanding of key concepts.
Step by stepSolved in 2 steps with 2 images

Knowledge Booster
Similar questions
- Scientists are in search of a mosquito repellant that is more effective. To test the effectiveness of the new compound versus the current compound, scientists have randomly selected 100 people to participate in their experiment. 100 bins, each with an equal number of mosquitoes in them, are available for the experiment. After a repellant is applied to a subject’s arm, they will insert theirforearm into a bin for 1 minute. The number of mosquito bites on the arm after 1 min will be counted. (IMAGE)) Write your answers in the box below. Make sure to identify which answer belongs to what question (e.g. Explanatory: variable a) Explanatory variable: Treatments: Response variable: Subjects/individuals: Design of Experiment:arrow_forwardy3D -V-aXarrow_forwardThe figure below shows the total number P(t) of Covid-19 cases in Minnesota¹ confirmed up to day t, where t = 0 is March 1, 2020. P (total cases) 5000 4000 3000 2000 1000 10 20 30 40 50 60 ¹Smoothed from JHU CSSE COVID-19 data at github.com/CSSEGISandData/COVID-19, accessed March 1, 2021. (a) What are the units of P (t)? OO days confirmed cases days per confirmed case confirmed cases per day t (days) (b) Estimate and compare P (30) and P (50). What does this tell you about the Covid-19 outbreak in Minnesota? P (30)~ i and P (50)~ This tells us thatarrow_forward
Recommended textbooks for you
- A First Course in Probability (10th Edition)ProbabilityISBN:9780134753119Author:Sheldon RossPublisher:PEARSON

A First Course in Probability (10th Edition)
Probability
ISBN:9780134753119
Author:Sheldon Ross
Publisher:PEARSON
