11. Suppose random variable X is distributed as normal with mean 2 and standard deviation 3 and random variable Y with mean 0 and standard deviation 4, what is the probability density function (pdf) of X + Y.
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![11. Suppose random variable X is distributed as normal with mean 2 and standard deviation 3 and
random variable Y with mean 0 and standard deviation 4, what is the probability density function
(pdf) of X + Y.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F5598c258-0b65-4f95-8bd3-29651964e95d%2Fc529d44f-d459-4ce5-ad3c-218630e0a494%2F3g8tkdr_processed.jpeg&w=3840&q=75)
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- Suppose that a random variable X is normally distributed with mean 2 and standard deviation 3 and a random variable Y is normally distributed with mean 0 and standard deviation 4. What is the probability density function of X+YLet grad be a dummy variable for whether a student-athlete at a large university graduates in five years. Let hsGPA and SAT be high school grade point average and SAT score, respectively. Let study be the number of hours spent per week in an organized study hall. i) Let 0( . ) be the standard normal cumulative distribution function and (· ) be the standard normal density function. Please write down the Probit model to describe the probability of graduating in five years in terms of hsGPA, SAT and study. Please write down the partial effect of study on P(grad = 1|hsGPA, SAT, study). (ii) If we use a Linear Probability Model instead, write down the model that you'll estimate. What limitations does this model have? (iii) Suppose that, using data on 420 student-athletes, the following logit model is obtained: P(grad = 1|hsGPA, SAT, study) =A(-1.17+ .24hsGPA+ .00058SAT+ .073study) where A(z) = exp(z)[1+ exp(z)]. Please give the expressions for P(grad = 1|hsGPA,SAT,study) P(grad =…If X is a random variable having a normal distribution with the mean μ and standard deviation σ, how do you show the moment generating function of Z=(X-μ)/σ is the moment generating function of the standard normal distribution?
- Suppose X is a randomvariable of normal distribution with mean equal to -2 and standard deviation equal to 4. Find P(X>-2)Q3/A/ Let X be a r.v with p.d.f f(x) = e - oPlease help me with this one. Thank you tutor!I For Poisson's distribution prove that Variance =Let x be a random variable that follows normal distribution with mean 5 and variance 16. Find P (210. Let F(x) - cumulative distribution function of the random variable . Find the cumulative distribution function and probability density function of the random variable F(5) .Show that the variance of a geometric random variable X; is given by V ar(X) = q/p^2 .If two independent sufficiently large samples are taken from two populations with known population standard deviations, the sampling distribution of the difference, sample mean (/x)1 - sample mean (/x)2 , between the two sample means /x1 and /x2 a. can be approximated by poisson distribution b. will have a variance of one. c. can be approximated by a normal distribution d. will have a mean of one. I would like to know why the answer is the answer and thank you.Recommended textbooks for youMATLAB: An Introduction with ApplicationsStatisticsISBN:9781119256830Author:Amos GilatPublisher:John Wiley & Sons IncProbability and Statistics for Engineering and th…StatisticsISBN:9781305251809Author:Jay L. DevorePublisher:Cengage LearningStatistics for The Behavioral Sciences (MindTap C…StatisticsISBN:9781305504912Author:Frederick J Gravetter, Larry B. WallnauPublisher:Cengage LearningElementary Statistics: Picturing the World (7th E…StatisticsISBN:9780134683416Author:Ron Larson, Betsy FarberPublisher:PEARSONThe Basic Practice of StatisticsStatisticsISBN:9781319042578Author:David S. Moore, William I. Notz, Michael A. FlignerPublisher:W. H. FreemanIntroduction to the Practice of StatisticsStatisticsISBN:9781319013387Author:David S. Moore, George P. McCabe, Bruce A. CraigPublisher:W. H. FreemanMATLAB: An Introduction with ApplicationsStatisticsISBN:9781119256830Author:Amos GilatPublisher:John Wiley & Sons IncProbability and Statistics for Engineering and th…StatisticsISBN:9781305251809Author:Jay L. DevorePublisher:Cengage LearningStatistics for The Behavioral Sciences (MindTap C…StatisticsISBN:9781305504912Author:Frederick J Gravetter, Larry B. WallnauPublisher:Cengage LearningElementary Statistics: Picturing the World (7th E…StatisticsISBN:9780134683416Author:Ron Larson, Betsy FarberPublisher:PEARSONThe Basic Practice of StatisticsStatisticsISBN:9781319042578Author:David S. Moore, William I. Notz, Michael A. FlignerPublisher:W. H. FreemanIntroduction to the Practice of StatisticsStatisticsISBN:9781319013387Author:David S. Moore, George P. McCabe, Bruce A. CraigPublisher:W. H. Freeman