Answered: [Q1] If the probability density… | bartleby

Related questions

Question

100%

[Q1] If the probability density function is f(x) as follows, find: (a) k that makes
f(x) a valid pdf, (b) Var(x).
f(x) = {***C-
Skx*(1- x) 0 <x<1
otherwise

Expert Solution

Step by step

Solved in 4 steps with 4 images

SEE SOLUTION Check out a sample Q&A here

Blurred answer

Similar questions

Find the expected value of the continuous random variable X associated with the probability density function over the indicated interval. 3 f(x)=x²; [0,8] 512 E(X)= 8 X
1.16. Establish thermodynamically the formulae v (7)= = S and v (R), V = N. Express the pressure P of an ideal classical gas in terms of the variables and 7, and verify the μl above formulae.
What is the probability that a number n, 1 ≤ n ≤ 99, is divisible by both 6 and 10? By either 6 or 10 or both?
Consider the function v(1,2) =( [1s(1) 3s(2) + 3s(1) 1s(2)] [x(1) B(2) + B(1) a(2)] Which of the following statements is incorrect concerning p(1,2) ? a. W(1,2) is normalized. Ob. The function W(1,2) is symmetric with respect to the exchange of the space and the spin coordinates of the two electrons. OC. y(1,2) is an eigenfunction of the reference (or zero-order) Hamiltonian (in which the electron-electron repulsion term is ignored) of Li with eigenvalue = -5 hartree. d. The function y(1,2) is an acceptable wave function to describe the properties of one of the excited states of Lit. Oe. The function 4(1,2) is an eigenfunction of the operator S,(1,2) = S;(1) + S,(2) with eigenvalue zero.
Show that the minimum cnergy of a simple harmonic oscillator is Fw/2 if ArAp = h/2, where (Ap)² = ((p - (p))?). %3D
A real wave function is defined on the half-axis: [0≤x≤00) as y(x) = A(x/xo)e-x/xo where xo is a given constant with the dimension of length. a) Plot this function in the dimensionless variables and find the constant A. b) Present the normalized wave function in the dimensional variables. Hint: introduce the dimensionless variables = x/xo and Y(5) = Y(5)/A.
The partition funetion for the ensemble characterized by constant V, E, and G = µÑ is given to a very good approximation by ø(V, E, µN)=Q(N,V,E)eBHN, where G = µN is the Gibbs energy (µ is the chemical potential and N is the average number of particles). Find an expression for the characteristic thermodynamic function for this ensemble in terms of the partition function ø(V, E, µN).
Please help to prove this to be true
2.3 (a) A classical harmonic oscillator p?, Kq? H + 2m 2 is in thermal contact with a heat bath at temperature T. Calculate the partition function for the oscillator in the canonical ensemble and show explicitly that • (E) = kgT, ((E – (E))²) = k¿T²
A student measures g, the acceleration due to gravity, repeatedly and carefully, and gets an answer of 9.5 m/s2 with an error bar of 0.1 m/s2. Assuming the measurements are distributed normally with a central value of the accepted 9.8 m/s2, what would be the probability of his getting an answer that differs from 9.8 m/s2 by as much as (or more than) this?Assuming he made no mistakes, do you think that his experiment may havesuffered from undetected systematic errors?
[c]
-a/2 1. [Particle in a box] If we shift the boundaries of the box to be at x = - and x = a/2, what will be the new form of the solution?

SEE MORE QUESTIONS