The speed of a molecule in a uniform gas at equilibrium is a random variable whose probability density function is given by f ( x ) = { a x 2 e − b x 2 x ≥ 0 0 x < 0 where b = m 2 k T and T, and in denote, respectively, Boltzmann’s constant, the absolute temperature of the gas, and the mass of the molecule. Evaluate a in terms of b.
The speed of a molecule in a uniform gas at equilibrium is a random variable whose probability density function is given by f ( x ) = { a x 2 e − b x 2 x ≥ 0 0 x < 0 where b = m 2 k T and T, and in denote, respectively, Boltzmann’s constant, the absolute temperature of the gas, and the mass of the molecule. Evaluate a in terms of b.
The speed of a molecule in a uniform gas at equilibrium is a random variable whose probability density function is given by
f
(
x
)
=
{
a
x
2
e
−
b
x
2
x
≥
0
0
x
<
0
where
b
=
m
2
k
T
and T, and in denote, respectively, Boltzmann’s constant, the absolute temperature of the gas, and the mass of the molecule. Evaluate a in terms of b.
Expression, rule, or law that gives the relationship between an independent variable and dependent variable. Some important types of functions are injective function, surjective function, polynomial function, and inverse function.
If the random variable Y has the following probability density
function
f(y) = {5
,0 < y< 5
,
(0,otherwise
The probability that the root of the function
g(x) = 4x² + 4yx + (y + 2) are real is
Let X and Y be independent random variables with joint probability density function fxy(x, y) = 1/3
(x + y), 0 < x <= 2, and 0 < y<= 1, and 0 otherwise. The marginal pdf fx(x) is given by
O a.
O b.
O c.
O d.
(2 +2X)/3
(2 + 2X)/3
(X+1/2)/3
(X+1/2)/3
0 < X<= 2
0< X<= 1
0 < X<= 1
0
Suppose that the random variables X and Y have the following joint probability density function.
f(x, y) = ce-6x-2y, 0 < y < x.
(a) Find the value of c.
(b) Find P(X < Y < 2)
,
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Continuous Probability Distributions - Basic Introduction; Author: The Organic Chemistry Tutor;https://www.youtube.com/watch?v=QxqxdQ_g2uw;License: Standard YouTube License, CC-BY
Probability Density Function (p.d.f.) Finding k (Part 1) | ExamSolutions; Author: ExamSolutions;https://www.youtube.com/watch?v=RsuS2ehsTDM;License: Standard YouTube License, CC-BY
Find the value of k so that the Function is a Probability Density Function; Author: The Math Sorcerer;https://www.youtube.com/watch?v=QqoCZWrVnbA;License: Standard Youtube License