Roughly, speaking, we can use probability density functions to model the likelihood of anevent occurring. Formally, a probability density function on (-, 0) is a function f suchthatf(x) > 0and| f(x) = 1.-0-(a) Determine which of the following functions are probability density functions on the(-00, 00).0 < x < e(i) f(x) =otherwise-20 < x < 2/2(ii) f(x) = { (x – v2)3otherwiseSledz0 < x < ∞(ii) f(x) =otherwisewhere A> 0(b) We can also use probability density functions to find the expected value of the outcomesof the event – if we repeated a probability experiment many times, the expected valuewill equal the average of the outcomes of the experiment. (e.g. S xf (x) dx yields theexpected value for a density f (x) with domain on the real numbers.) Find the expectedvalue for one of the valid probability densities above.

Answered: oughly, speaking, we can use…

MATLAB: An Introduction with Applications

6th Edition

ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

Chapter1: Starting With Matlab

Section: Chapter Questions

Problem 1P

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With the known values of a = 200,000 and b = 230,000, the first equation for the probability density function for the sales price of a home is found as follows. f(x) = 1/b – a, a ≤ x ≤ b = 1/230,000 − 200000, 200,000 ≤ x ≤ 230,000 = 1/30000, 200,000 ≤ x ≤ 230,000 Everywhere else, the probability density function will just be 0. Therefore, the full probability density function for the sales price of a home follows. f(x) = _______________ 200,000 ≤ x ≤ 230,000 elsewhere
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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Suppose a college professor never finishes her lecture before the end of the class period, and always finishes within five minutes after the class period is supposed to end. Let X = time that elapses between the end of the class period and the actual end of the lecture. Suppose the pdf of X is: (image) Find the value of k that makes f(x) a legitimate probability density function, and use that value of k to find the probability that the lecture ends less than 3 minutes after the class period is supposed to end.
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