A dataset is collected, giving the values [1.2, -3 4.1]. Construct a RV y whose PDF has the same outcomes. Use the Dirac Delta 8(y - yn) in your response. This an important concept.
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![A dataset is collected, giving the values [1.2, -3 4.1]. Construct a RV y whose PDF has the
same outcomes. Use the Dirac Delta 8(y – Yn) in your response. This an important concept.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F4ccd578f-522c-45d7-b87e-2858428fb795%2F2a4964a4-bf91-4bc3-9ab9-46f2fd05e098%2Feegq3r_processed.jpeg&w=3840&q=75)
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- find the integrate(v . dr) of the following case:The vertical displacement v of a cracked slurry infiltrated fiber concrete member at maximum shear stress is given by v = a + bw, where w is the crack width, and a and b are estimated from data to be a = 2.5 ± 0.1 mm and b = 0.05 ± 0.01. Assume that w = 1.2 ± 0.1 mm.a) Estimate v, and find the uncertainty in the estimate.b) Of the uncertainties in w, a, and b, only one has a non-negligible effect on the uncertainty in v. Which one is it?Suppose that a person’s score X on a mathematics aptitude test is a number between 0 and 1 and that his score Y on a music aptitude test is also a number between 0 and 1. Suppose further that in the population of all college students in Belize, the scores X and Y redistributed according to the following joint pdf. f(x,y) = 2/5(2x + 3y) for 0≤x≤1, 0≤y≤1 and 0 otherwise What proportion of college students obtain a score greater than 0.8 on the mathematics test? If a student’s score on the music test is 0.3, what is the probability that his score on the mathematics test will be greater than 0.8?
- Can you find the amount of salt A in the tank at any time t?The volume of a cylinder is given by V = πr²h, where r is the radius of the cylinder and h is the height. Assume the radius, in cm, is lognormal with parameters μr = 1.6 and σ²r = 0.04 , the height, in cm, is log-normal with parameters μh = 1.9 and σ²h = 0.05, and that the radius and height are independent. a) Show that V is lognormally distributed, and compute the parameters μV and σ²V. (Hint: ln V = ln π+2 ln r + ln h.) b) Find P(V < 600). c) Find P(500 < V < 800). d) Find the mean of V. e) Find the median of V. f) Find the standard deviation of V. g) Find the 5th percentile of V. h) Find the 95th percentile of V.Define each of the following: the tangential component ofacceleration, the normal component of acceleration, andcentripetal acceleration. How are each of these quantitiescomputed?