Roughly, speaking, we can use probability density functions to model the likelihood of an event occurring. Formally, a probability density function on (-∞, ∞) is a function f such that f(x) > 0 and f (x) = } (a) Determine which of the following functions are probability density functions on the (-00, 00). |x-1 0 < x < e (i) f(x) = otherwise -2 0 < x < 2/2 (ii) f(x) = (x – /2)3 - otherwise dedæ 0 0 (b) We can also use probability density functions to find the expected value of the outcomes of the event – if we repeated a probability experiment many times, the expected value will equal the average of the outcomes of the experiment. (e.g. xf (x) dx yields the expected value for a density f(x) with domain on the real numbers.) Find the expected value for one of the valid probability densities above.
Roughly, speaking, we can use probability density functions to model the likelihood of an event occurring. Formally, a probability density function on (-∞, ∞) is a function f such that f(x) > 0 and f (x) = } (a) Determine which of the following functions are probability density functions on the (-00, 00). |x-1 0 < x < e (i) f(x) = otherwise -2 0 < x < 2/2 (ii) f(x) = (x – /2)3 - otherwise dedæ 0 0 (b) We can also use probability density functions to find the expected value of the outcomes of the event – if we repeated a probability experiment many times, the expected value will equal the average of the outcomes of the experiment. (e.g. xf (x) dx yields the expected value for a density f(x) with domain on the real numbers.) Find the expected value for one of the valid probability densities above.
Calculus For The Life Sciences
2nd Edition
ISBN:9780321964038
Author:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.
Publisher:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.
Chapter9: Multivariable Calculus
Section9.4: Total Differentials And Approximations
Problem 23E: Eastern Hemlock Ring shake, which is the separation of the wood between growth rings, is a serious...
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