Psi (x) = A exp (-|x|/a) . Find A using normalisation
- A() An electron is in the spin state x= A Determine the normalisation constant 1 i A, and then find the expectation value of the z-component of the spin operator h [6]
using the complex form of a electromagentic wave, derive the jones vector ans show the normalisation of the general vector.
Find the derivative 1.) X(+) = cos(+²) 2.) X(t) = cos(( exp (-+)7²) 3.) × (t) = cos(-exp (+²) 4.) X(t) = cos (exp(+²)) sin(t) s.) X(t) = cos (cos(+)) exp(-t)
4.3-17. Find the marginal densities of X and Y using the joint density Sx.x(x,y) = 2u(x)u(v)exp- anos a b 4.3-19. The joint density of two random variables X and Y is E fx.y(x,y) = 0.18(x)8(y)+0.128(x - 4)8(y) Problem +0.058(x)(y-1) +0.258(x-2)(y-1) valaltitude +0.38(x-2)8(y - 3) +0.188(x-4)8(y - 3) Find and plot the marginal distributions of X and I.
6) Use MATLAB and Newton-Raphson method to find the roots of the function, f(x) = x-exp (0.5x) and define the function as well as its derivative like so, fa@(x)x^2-exp(.5%), f primea@(x) 2*x-.5*x"exp(.5%) For each iteration, keep the x values and use 3 initial values between -10 & 10 to find more than one root. Plot each function for x with respect to the iteration #.
EXP #12: PRE-LAB EXERCISE 1. A sample of a gas has a pressure of 23.8 PSI and a volume of 250 mL. If the volume is increased to 1.50 L, what will the new pressure be? Show your calculations. 2. Doctor Stanley Schmozawitz measures the tire pressure on his recumbent bike one morning when it is 41.0 degrees Fahrenheit (5.0 degrees Celsius) and finds it to be 55 PSI. Later that afternoon, it is 77.0 degrees Fahrenheit (25.0 degrees Celsius),...
Suppose X ~ Exp(); f(X/)
= e^(-x)
, x > 0 and we have n=1
Find an unbiased estimate of 1/
Find an unbiased estimate of 1/(^2)
Psi(x) = {Ax(a-x), for 0 lessthanorequalto X lessthanorequalto A otherwise Psi(x) to compute value of A Calculate the expectation value of the energy association with this state. Recall that <E>= integral^infinity_-infinity Psi*h Psi dx HERE h = -H^2/2M D^2/DX^2 + v
) Let Y ∼ Exp(λ). Given that Y = m, let X ∼ Pois(m).
Find the mean and
variance of X.
estrbetrecoralcional stribution. 2. (Anderson, 10, 11) Let Y ~ Exp(A). Given that Y = m, let X ~ Pois(m). Find the mean and variance of X 3 (Anderson 10
(25 marks) Consider a wave packet defined by \(\psi(x)=\int_{-\infty}^{\infty} A(k) \cos k x d k,\) where \(A(k)\) is given by$$ A(k)=\left\{\begin{array}{ll} 1 & \text { for } 0 \leq k \leq k_{0} \\ 0 & \text { otherwise } \end{array}\right. $$The width of \(A(k)\) is thus equal to \(\Delta k=k_{0}\). (a) Determine the function \(\psi(x)\). (b) What is the value of \(\psi(0) .\) (c) Sketch the function \(\psi(x)\). (d) The function \(\psi(x)\) is sharply peaked at \(x=0\). Define the width...