15 Help me answer the question If X is a continuous random variable, argue that P(x < X < x2) = P(x1 < X < x2) = P(x1 < X < x2) = P(x1 < X < x2).%3DX2Because in the integral / f(x) dx the functionf(x) in any of the endpoints x, and x2 is always equal to zero, all theprobabilities listed are equal.O These probabilities are not equal.Because the probabilities P(X = x1), P(X = x2) are approximately equal to zero, all the probabilities listed are equal.Because the probabilities P(X = x1) = P(X = x2) = 0, all the probabilities listed are equal.

in the continuous random variables “≤” and “<”, and similarly“≥” and “>”, are interchangeable.…

Answered: If X is a continuous random variable,…

Algebra & Trigonometry with Analytic Geometry

13th Edition

ISBN:9781133382119

Author:Swokowski

Publisher:Swokowski

Chapter9: Systems Of Equations And Inequalities

Section: Chapter Questions

Problem 52RE

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A certain experiment produces the data (0, 1),(−1, 2),(1, 0.5),(2, −0.5). Find values for a, b, and c which describe the model that produces a least squares fit of the points by a function of the form f(x) = ax2 + bx + c.
1. Linearize x³ + In x about x=3
(b) Let X₁, X₂, X3 be uncorrelated random variables, having the same variance ². Consider the linear transformations Y₁ = X₁ + X₂, Y₂ = X₁ + X3 and Y3 = X₂ + X3 . Find the correlations of Yi, Y; for i #j. (5 marks)
There are only two states of the world, when a person is well with probability (1-p) and ill with probability p, where (1-p)= 1/3 and p = 2/3. Consider Adam who has utility function U = (Y1, Y2,1 – p,p) = Y,"-P)Y?, where Y; is the income and i =1 is well and i = 2 is ill. When Adam is well, he earns $1000, but when he is ill, he losses $300 in health expenditures and earnings such that Y2 = $700. What is the maximum total premium that Adam is still willing-to-pay? (1-р).
Two drunk start out together at the origin, each having the equal probability of making a step to the left or right along the x-axis. Assume that men make their steps simultaneously. Let N be the total number of steps taken by each man. Assume that a particular instant, they are separated by some distance. In this situation, in a given particular step. If they move towards each other, the separation between them decreases. If the move away from each other, the separation between them increases If they move in the same direction, the separation remains unaltered Out of N steps, n1 steps belong to decreasing the separation of them; n2 steps belong to increasing the separation of them and n3 steps belong to no separation. Then, calculate the following. (a) The probability of taking the steps n1, n2 and n3 (b) The probability that they meet again at N steps
Two drunk start out together at the origin, each having the equal probability of making a step to the left or right along the x-axis. Assume that men make their steps simultaneously. Let N be the total number of steps taken by each man. Assume that a particular instant, they are separated by some distance. In this situation, in a given particular step. If they move towards each other, the separation between them decreases. If the move away from each other, the separation between them increases If they move in the same direction, the separation remains unaltered Then calculate (a) The probability of decreasing their separation (b) The probability of increasing their separation (c) The probability of no separation between them Out of N steps, n1 steps belong to decreasing the separation of them; n2 steps belong to increasing the separation of them and n3 steps belong to no separation. Then, calculate the following. (d) The probability of taking the steps n1, n2 and n3 (e) The…
Let X and Y be random variables with variances Var(X) = 1 and Var(Y ) = 2. (Note that X and Y might not be independent.) What is the maximum possible value of Var(3X − 2Y + 4)?
Suppose that X₁, X2, X3 are independent and identically distributed random variables with distribution function: Fx (x) = 1 – 3¯ª for x ≥ 0 and Fx (x) = 0 for x 1).
Consider a logistic regression system with two features x1 and x2. Suppose 00 = 5, 01 = 0, 02= 0, 03= -5, 04= -1, draw the decision boundary of hø(x) = g(0+ 01 x1+ 02 X2 + 03 xı²+ 04 x2?).
The diameter of a round rock in a bucket, can be messured in mm and considered a random variable X in f(x) f(x) = k(x-x4) if 0 ≤ x ≤ 1f(x) = 0 otherwise. determine the constant k such that the set is valid.
Let Y₁ = (x,-X₂), where X, and X₂ are independent random variables and each of them X, 2 is distributed as x² (2). Find the p.d.f. of Y₁.

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