Let Z ∼ N(0,1) and Y = Z1/3 (a) Find the density function (pdf) of Y . b) FindP (Y> (1/4)^1/3))
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Let Z ∼ N(0,1) and Y = Z1/3
(a) Find the density
b) FindP (Y> (1/4)^1/3))
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- If (Y(t)} is the square law detector process and if Z(1) = Y(t) – E{Y(t)}, show that 1 the spectral density of {Z(r)} is given by S„@) : | S@) S„(@- a) da, where S,(@) is the input spectral density.The joint pdf of two variables X,Y is fxy(x,y)=ae*+y) for x20, y>0. Find the constant a. Are X and Y independent?2. A particle of mass, m, has the wavefunction given by: (x, t) = Ce-a[(mx²/h) + it] . (a) Sketch Re [(x,0)] as a function of x. (b) Sketch Re [p(0, t)] as a function of t. (c) Sketch the probability density for finding the particle at x at t = 0. (d) Explain the time dependence in the probability density for locating the particle in space. (e) Find C (f) Find (x) (g) Find (x2) (h) Find ox (i) Find (p) (j) Find (p?) (k) Find op (1) Is the product, O,0, consistent with the Heisenberg uncertainty principle? (m) Find T
- Let X, Y have the joint density function 2 \exp(-x-y) if Are they independent? Find Cov(X,Y). 05) For the following density function f(x) = c x2 (1–x), 0#2, Suppose that X and Y have joint density given by: f (x, y) = 15x²y, 0 < x < y < 1. (a) Find the marginal pdf of Y. (b) Find the conditional pdf of X given Y. (c) Find the conditional expectation of X given Y = 1/3. (d) Are X andY independent? Show this in two different ways. (e) Give an integral expression for P(X + 2Y < 1), but do not evaluate it.Recommended textbooks for youA First Course in Probability (10th Edition)ProbabilityISBN:9780134753119Author:Sheldon RossPublisher:PEARSON
A First Course in Probability (10th Edition)ProbabilityISBN:9780134753119Author:Sheldon RossPublisher:PEARSON