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Problem 1) The cumulative distribution function of random variable X is: 0 x<-1 x + 1 Fx(x) = a) Find P[X > 1/2]. b) Find P[-1/2 < X ≤ 3/4]. c) Find P[|X| ≤ 1/2]. 2 1 -1

Problem 1) The cumulative distribution function of random variable X is: 0 x<-1 x + 1 Fx(x) = a) Find P[X > 1/2]. b) Find P[-1/2 < X ≤ 3/4]. c) Find P[|X| ≤ 1/2]. 2 1 -1

Linear Algebra: A Modern Introduction
Linear Algebra: A Modern Introduction
4th Edition
ISBN:9781285463247
Author:David Poole
Publisher:David Poole
Chapter2: Systems Of Linear Equations
Section2.4: Applications
Problem 1EQ: 1. Suppose that, in Example 2.27, 400 units of food A, 600 units of B, and 600 units of C are placed...
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Problem 1) The cumulative distribution function of random variable X is: 0 x<-1 x + 1 Fx(x) a) Find P[X > 1/2]. b) Find P[-1/2 < X < 3/4]. c) Find P[IX ≤ 1/2]. Problem 2) The CDF of random variable Wis 0 w +5 d) What is the value of a such that P[X ≤ a] = 0.8. e) Find the PDF fx (x) of X. Fw (w) = a) Find the constant c. b) Find P[0 ≤ x ≤ 1]. 1 c) Find P[-1/2 ≤ X ≤ 1/2]. d) Find the CDF Fx (x). 1 4 1 Define the random variable Y by Y a) Find E[X] and Var[X]. b) Find h(E[X]) and E[h(X)]. c) Find E[Y] and Var[Y]. 8 + 2 1 3(w - 3) 8 -1<x< 1 x ≥ 1 a) Find P[W≤ 4]. b) Find P[-2 < W ≤ 2]. c) Find P[W > 0]. d) What is the value of a such that P[Wa] = 0.5. Problem 3) The random variable X has the following probability density function: fx(x) = {cx = h(x) x <-5 -5 ≤w <-3 -3 ≤w <3 = 3 ≤w<5 w ≥ 5 Problem 4) Continuous random variable X has the following PDF: -1≤x≤3 fx(x) = 4 otherwise X² CX 0≤x≤2 otherwise
Transcribed Image Text:Problem 1) The cumulative distribution function of random variable X is: 0 x<-1 x + 1 Fx(x) a) Find P[X > 1/2]. b) Find P[-1/2 < X < 3/4]. c) Find P[IX ≤ 1/2]. Problem 2) The CDF of random variable Wis 0 w +5 d) What is the value of a such that P[X ≤ a] = 0.8. e) Find the PDF fx (x) of X. Fw (w) = a) Find the constant c. b) Find P[0 ≤ x ≤ 1]. 1 c) Find P[-1/2 ≤ X ≤ 1/2]. d) Find the CDF Fx (x). 1 4 1 Define the random variable Y by Y a) Find E[X] and Var[X]. b) Find h(E[X]) and E[h(X)]. c) Find E[Y] and Var[Y]. 8 + 2 1 3(w - 3) 8 -1<x< 1 x ≥ 1 a) Find P[W≤ 4]. b) Find P[-2 < W ≤ 2]. c) Find P[W > 0]. d) What is the value of a such that P[Wa] = 0.5. Problem 3) The random variable X has the following probability density function: fx(x) = {cx = h(x) x <-5 -5 ≤w <-3 -3 ≤w <3 = 3 ≤w<5 w ≥ 5 Problem 4) Continuous random variable X has the following PDF: -1≤x≤3 fx(x) = 4 otherwise X² CX 0≤x≤2 otherwise
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