# 1) Determine 1-234(expl-2x2))dx #2) Let's assume that only Ф table is available, find erf(-2). #3)...
234 = 9 marks ] Question 3 Work in 1-dimension for simplicity. Let ф(2', t) %3DT(2", 2)ф(т, t), where T(',x) is called the "space translation operator from x to x". so that r' = x + dx. Explain why the following form makes (a) Consider an infinitesimal space translation, sense for the corresponding "infinitesimal space translation operator": idx T(xdr, x) 1 + ô+ (dx2) (b) Hence show that O is the momentum operator. (c) Explain why the full space translation...
A Gaussian random variable X has mean 2 and variance 4 a) Find P(X < 3). (b) Find P(1 < X < 3) (c) Find P({X > 4}|{X > 3}) (d) Let Y = X^2 . Find E[Y].
Consider a Gaussian random variable X with mean 8 and variance 3. Find z if P[X>10]=1- (phi)(Z)
a) Find the eigenvalues and the eigenvectors of the 2x2 matrix: [4 2] [3 -1] b) Solve the initial value problem: dx/dt = 4x + 2y dy/dt = 3x - y with x(0) = 0, y(0) = 7
e.) Find and sketch the PSD of V(t). What does the system in Fig. 1 do? Problem 4 (10 points, Graduate Students Only). Suppose X is a binary random variable, with PIX = ol = 0.8 and PIX = 1] = 0.2. Suppose Y is a Gaussian random variable conditioned on X. Specifically, when X 0, py)x (ulz) is a Gaussian distribution with 0 mean and variance σ2. Similarly, when X-1, prix(ylz) Is a Gaussian distribution with mean A (A...
144r2+49 -da 1. Find 144x2 +49 144x2 + 49 dx- dx *+C (145x2 +5033/2 4322" -+CO (144x2 + 49,3/2 147x? -+Co 3/2 - + 98x4 (13x2+8,972 147x (169x2+61) 1447 •dx- - 144x2 +49 os dx- 14 144x2 + 49 ·da- + 1 - 1 2. Find the indefinite integral a zona de *Cp the +Or arada?4+cr het oor HC I - dx 3.Complete the square and find ' *x?+24x + 156 dx = 12: +24x+156 + (x + I Tp2...
The random variable X takes only the values 0, ±1, ±2. In addition, it is known that P(-1 <X <2) 0.2 P(X = 0) = 0.05 PCI 1) = 0.35 P(X 2) = P(X = 1 or-1) (a) Find the probability distribution of X (b) Compute E[X]
calculo 1- Given the function y = (4-x^2 ) + 4 * arcsen (x/2) Get dy/dx and its value for x 0 (this year is requested to find the value of the pending for the function given in Point X :0). 2- Is yarcta n ((x +3)/(1-3x) Find his derivative 3- Determine dy,/ dx and the value at the point (using implied derivation) 2x 2 y 2-3xy 1 0 3x2Уз + 3xy2 +1-6+,5 2xy + sen(y) # 2 6 Determine...
Consider the sample space S = {-3,-1, 0, 2, 4} and the events A = {-1, 0}, B = {0, 2}, and C = {-3, 0, 4} derived from the discrete random variable X. Let the probability of each outcome be as listed in the table below. Outcome (X) Probability −3 0.10 −1 0.20 0 0.30 2 c 4 0.25 Outcome (X) l Probability -3 0.10 -1 0.20 0 0.30 2 c 4 0.25 a) Find the value of the...
The table below represents the probability density function for the rain available X find the standard deviation of X ng Numbers Calcula + earn/course/Saa1a356-2cd6-4fc4-9700-47b2031814c4/assignment/5168e143-84c3-443a-bc96-98d4dc647876 d the Standard Deviation of a Discrete Random Variable From Its Probability Density Function Question The table below represents the probability density function for the random variable X. Find the standard deviation of X Round the final answer to two decimal places. POX x) X 0 1/6 4 1/3 8 1/2 O Help nCopy to Clipboard...