Suppose a research paper states that the distribution of the daily sea-ice advance/retreat from each sensor is similar and is approximately double exponential. The proposed double exponentialdistribution has density function f(x) = 0.5le¬A]XI for -∞ < x < ∞. The standard deviation is given as 40.9 km. (Round your answers to four decimal places.)(a) What is the value of the parameter å?(b) What is the probability that the extent of daily sea-ice change is within 1 standard deviation of the mean value?

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Answered: Suppose a research paper states that…

Linear Algebra: A Modern Introduction

4th Edition

ISBN:9781285463247

Author:David Poole

Publisher:David Poole

Chapter7: Distance And Approximation

Section7.3: Least Squares Approximation

Problem 33EQ

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Suppose a research paper states that the distribution of the daily sea-ice advance/retreat from each sensor is similar and is approximately double exponential. The proposed double exponential distribution has density function f(x) = 0.5?e−?|x| for −∞ < x < ∞. The standard deviation is given as 41.2 km. a. What is the value of the parameter ?? b. What is the probability that the extent of daily sea-ice change is within 1 standard deviation of the mean value?
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For a certain psychiatric clinic suppose that the random variable X represents the total time (in minutes) that a typical patient spends in this clinic during a typical visit (where this total time is the sum of the waiting time and the treatment time), and that the random variable Y represents the waiting time (in minutes) that a typical patient spends in the waiting room before starting treatment with a psychiatrist. Further, suppose that X and Y can be assumed to follow the bivariate density function fXY(x,y)=λ2e−λx, 0<y<x, where λ > 0 is a known parameter value. (a) Find the marginal density fX(x) for the total amount of time spent at the clinic. (b) Find the conditional density for waiting time, given the total time. (c) Find P (Y > 20 | X = x), the probability a patient waits more than 20 minutes if their total clinic visit is x minutes. (Hint: you will need to consider two cases, if x < 20 and if x ≥ 20.)
suppose x has an exponential distribution with probability density function f(x) =2e^-2x, x>0. Then P(X>1)
Suppose a research paper states that the distribution of the daily sea-ice advance/retreat from each sensor is similar and is approximately double exponential. The proposed double exponential distribution has density function f(x) = 0.5?e−?|x| for −∞ < x < ∞. The standard deviation is given as 40.6 km. (Round your answers to four decimal places.) (b) What is the probability that the extent of daily sea-ice change is within 1 standard deviation of the mean value? Note: 0.4386 is not the answer
Suppose that X is a continuous unknown all of whose values are between -5 and 5 and whose PDF, denoted f, is given by f ( x ) = c ( 25 − x^2 ) , − 5 ≤ x ≤ 5 , and where c is a positive normalizing constant. What is the expected value of X^2?
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