Roughly, speaking, we can use probability density functions to model the likelihood of anevent occurring. Formally, a probability density function on (-0, 0) is a function f suchthatf(x) > 0and| f(x) = 1.%3D(a) Determine which of the following functions are probability density functions on the(-0, 00).(i) ƒ(x) =0.ə > x > 0 1-x]otherwise-20 < x < 2/2(ii) f(x) = { (x– v2)3%3Dotherwisededze0 < x < ∞(iii) f(x) =0.otherwisewhere X> 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. Srf(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.

(a) Determine which of the following functions are probability density functions on the (-00, 00). x- 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. rf(x) da 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.

(a) Determine which of the following functions are probability density functions on the (-00, 00). x- 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. rf(x) da 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.

Functions and Change: A Modeling Approach to College Algebra (MindTap Course List)

6th Edition

ISBN:9781337111348

Author:Bruce Crauder, Benny Evans, Alan Noell

Publisher:Bruce Crauder, Benny Evans, Alan Noell

Chapter1: Functions

Section1.2: Functions Given By Tables

Problem 11E: A Troublesome Snowball One winter afternoon, unbeknownst to his mom, a child bring a snowball into...

See similar textbooks

Similar questions

Recall that the general form of a logistic equation for a population is given by P(t)=c1+aebt , such that the initial population at time t=0 is P(0)=P0. Show algebraically that cP(t)P(t)=cP0P0ebt .
A Troublesome Snowball One winter afternoon, unbeknownst to his mom, a child bring a snowball into the house, lays it on the floor, and then goes to watch T.V. Let W=W(t) be the volume of dirty water that has soaked into the carpet t minutes after the snowball was deposited on the floor. Explain in practical terms what the limiting value of W represents, and tell what has happened physically when this limiting value is reached.
suppose x has an exponential distribution with probability density function f(x) =2e^-2x, x>0. Then P(X>1)
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
If X is a continuous variable in the range 3 > X > 0 and its distribution function is as follows: F ( x ) = k : ( x3 + x2) find the probability density function?
The life (in years) of a laptop battery has a probability density function defined by P(x)=12e−x/2P(x)=12e-x/2for x in [0,∞)[0,∞). Find the probability that a randomly selected laptop battery will last between 3 and 8 years?
Suppose that the unknown X is ≥ 2 and has the probability density function fX(x)=Ce^−x,x ≥ 2.What is the numerical value of C?
Find a value of k that will make f a probability density function on the indicated interval. ƒ(x) = kx; [2, 4]
Find a value of k that will make f a probability density function on the indicated interval.ƒ(x) = kx; [2, 3]
Verify that p(x) = 3x - 4 is a probability density function on [1, oo)and calculate its mean value.
Show that f(x)f(x) is a probability density function,
Suppose that the joint probability density function of X and Y is fX,Y(x,y) = 10.125(x2 – y2) e−3x , for 0<x<∞ and -x<y<x 0, otherwise Give your answers to the below questions in two decimal places where appropriate. (a) The marginal probability density function of X is given by: fX(x) = A xB e-3x , for 0<x<∞ 0, otherwise Find the value of A. (b) Find the value of B. (c) The conditional probability density function of Y, given that X=x for some x>0, takes the following form: fY|X=x(y) = C (x2-y2) xD e-Ex, for -x<y<x 0, otherwise. Find the value of C (d)Find the value of D. (e)Find the value of E.