3.7.23. Suppose that X and Y are discrete random vari-ables with4!y4-x-yPx.x (x, y) = x!y! (4 + x - y)! (2) O.)'()'(3-0≤x+y≤4Find px (x) and py(x).

Given: PX=x,Y=y=4!x!y!4-x-y!12x13y164-x-y 0≤x+y≤4

Answered: 3.7.23. Suppose that X and Y are…

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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IV) When a current X amperes flows through a resistance Y ohms, the power generated is given by w=x²y watts. Suppose the current and resistance are independent random variables with densities b = f(x)=6x (1-x), 0≤x≤1 X If the CDF of Wis Fw (w) = wª +6w - 8w 3/2, b ≤w ≤c, where a, b and care constants then a = C= fy(y)=2y, 0≤x≤1
6
Logan and Brian began arguing about who did better on their tests, but they couldn't decide who did better given that they took different tests. Logan took a test in Art History and earned a 76.8, and Brian took a test in English and earned a 68.9. Use the fact that all the students' test grades in the Art History class had a mean of 71.9 and a standard deviation of 11.6, and all the students' test grades in English had a mean of 61 and a standard deviation of 9.4 to answer the following questions.a) Calculate the z-score for Logan's test grade.z=z= [Round your answer to two decimal places.] b) Calculate the z-score for Brian's test grade.z=z= [Round your answer to two decimal places.]c) Which person did relatively better? Logan Brian They did equally well.
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4. A particle moves on the x- axis starting at x = 0. With equal probability, the particle moves to the left or right one unit. Let X denote the position on the x- axis after four moves. (a) Find px(x). Notice that X can take on -4,-2,0, 2, 4. Fill out the table below. xPx(x) (b) What is the expected position of the particle after four moves. That is, compute E(X). Express your answer as a fraction in lowest terms.
1. Given that X~N(39,32)A Random variable X is normally distributed and has a mean of 9 C Random variable X is not normally distributed and the mean is 39 B Random variable X is normally distributed and has a mean of 3 D Random variable X is normally distributed and the mean is 39
17. If X is uniformly distributed continuous random variable over [1, 3], then * 4/3 S14 2/3 -19
24. Gaussian random variables X, and X,, for which, X, = 2, o = 9, X, =-1, ox, = 4 and Cxx, =-3, are transformed to new random variables Y, and Y, according to जापर डेरें| Y, =-X, + X, Y, =-2X,- 3X, (iii) Cy,Cy, .. Find
4 Suppose that Alejandro is planting a garden of tulips. Let X be the Bernoulli random variable that returns 1 if the tulip is red, and 0 otherwise. Suppose Y is another Bernoulli random variable, independent of X, that returns 1 if the tulip survives longer than 30 days, and 0 otherwise. Both X and Y have parameters 1/2. Let Z be the random variable that returns the remainder of the division of X +Y by 2. For example, if X = 1 and Y = 0, Z = remainder() = 1 (a) Prove that Z is also a Bernoulli random variable, also with parameter 1/2. (b) Prove that X, Y, Z are pairwise independent but not mutually independent. (c) By computing Var[X+Y+Z] according to the alternative formula for variance and using the variance of Bernoulli r.v.'s, verify that Var[X+Y+Z] = Var[X]+Var[Y] +Var[Z] %3D (observe that this also follows from the proposition on slide 5 of the lecture segment entitled "Binomial distribution").
4. The distribution function of a random variable W is given by: Oforw 2 a. Find P (1 < w< 3). Enter probability as a reduced fraction. prob = %3D b. Find f(w). Enter coefficients as reduced fractions and express powers with ^. f(w) 3= for -2< w < 2 %3D

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3.7.23. Suppose that X and Y are discrete random va ables with 4-x-y PX,Y (x, y) = *(4-x-)!()*()'()* x!y!(4- x - y)! 2 3 0≤x+y≤4 Find px (x) and py(x).

3.7.23. Suppose that X and Y are discrete random va ables with 4-x-y PX,Y (x, y) = (4-x-)!()()'()* x!y!(4- x - y)! 2 3 0≤x+y≤4 Find px (x) and py(x).