Prove the follawing:(a) E (Č X) = CE(X) (b) E (X + Y) = E(X) + E(Y) (c) E (XY) = E(X) · E(Y)When X and Y are statistically independent.%3D

Answered: Prove the following: (a) E (C X) = Č…

MATLAB: An Introduction with Applications

6th Edition

ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

Chapter1: Starting With Matlab

Section: Chapter Questions

Problem 1P

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Exercise 5. Let X be a r.v. representing the outcome of rolling a fair, 6-sided die: ƒ(1) = ƒ(2) = = = f(6) = 1/6. (a) Verify explicitly that E(X) = 3.5. (b) Calculate E(X²), and verify that E(X²) is not the same as the square of E(X).
(a) According to experimental data, the intensity of scattered sunlight in the atmosphere I is inverse proportional to the wavelength in the power n, 1 = A/2". Consider the pseudo-experimental data shown in the Table where and I are presented in the normalized dimensionless variables. (b) 2 350 400 450 500 550 600 650 700 750 800 I 6.1.10 4.9-10 1.9-10 2.1-10 6.5-10 9.3-106 6.5-10 3.5-10 3.8-10° 2.5-106 Using the statistical analysis, determine the exponent n and constant A. Present the result with the determined constants in the form I(2) = A2™". (c) Present the plot 1(2) in the log-log scale. Show the data given in the table and best fit line.
2х — е - Let g(x) = What is g'(e)? %3D In x
a. f(x2 – 1)e*-3x dx
Given P(E) = 0.96, what is P(E')?
1. You have the following PDF: f(x) = { 1≤x≤e. (a) Find the value of c such that this is a valid PDF. (b) Calculate E(X). (c) Calculate V(X). (d) Calculate F(x).
For the function g(1) = (8t + 1) In t we have g' (1) = -- %3D Select one: True O False
1/2 If f(x) = g(x) ·x2, g(4) = 8, and g' (4) = 2, then f'(4) =? %3D %D Select one: 17/2 6. 16 8.
Complete the missing information for this regression model (df= 23). Y' 1.0 X, .50 X, 25.1 1.2 X, + + (2.1) (1.5) (1.3) (.06) standard errors () () () (11.9) () t ratios () () Significant at .05?
1. Fix r € N, and suppose that Y₁,..., Yn are independent and identically distributed NegBin(r, ) random variables, each with probability mass function given by ¡v (u | 0) – (1 + r − ¹) (1 - fy y (1 - 0) ³0⁰ for y ¤ N and unknown 0 € (0, 1). Here the number of successes r in the negative binomial is known.
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Problem: Consider the pdf of the rv Y |4/25 12/5 -4/25 () < y < 5 f(y) (a) obtain the cdf of Y (b) calculate the 100p-th percentile of Y (c) calculate E(Y) ↑fi4)→ pd

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Prove the following: (a) E (C X) = Č E(X) (b) E (X + Y) = E(X) + E(Y) (c) E (XY) = E(X) · E(Y) When X and Y are statistically independent. %3D