This problem involves two continuous random variables X and Y with joint pdf given by J6x, x, y ≥ 0 and x+y≤1 fx,y(x, y) = 0, otherwise. That is, over the shaded region below, we have fx,y(x, y) = 6x. y (0,1) x (1,0) We can check that this is a valid joint pdf by integrating over the shaded region: .1 [ƒx,y (x, y) dx dy = [[ 6x dx dy = 1. (a) Let A denote the event {X <0.5}. Find the conditional pdf fx|A(x). (b) What is P(X + Y ≤ 1)? (c) What is P(X + Y ≤ 0.5)? (d) Let Z=XY. Find fz(z), the pdf of Z. Hint 1: X and Y are not independent. Hint 2: start by finding the cdf of Z.

This problem involves two continuous random variables X and Y with joint pdf given by J6x, x, y ≥ 0 and x+y≤1 fx,y(x, y) = 0, otherwise. That is, over the shaded region below, we have fx,y(x, y) = 6x. y (0,1) x (1,0) We can check that this is a valid joint pdf by integrating over the shaded region: .1 [ƒx,y (x, y) dx dy = [[ 6x dx dy = 1. (a) Let A denote the event {X <0.5}. Find the conditional pdf fx|A(x). (b) What is P(X + Y ≤ 1)? (c) What is P(X + Y ≤ 0.5)? (d) Let Z=XY. Find fz(z), the pdf of Z. Hint 1: X and Y are not independent. Hint 2: start by finding the cdf of Z.

Introductory Circuit Analysis (13th Edition)

13th Edition

ISBN:9780133923605

Author:Robert L. Boylestad

Publisher:Robert L. Boylestad

Chapter1: Introduction

Section: Chapter Questions

Problem 1P: Visit your local library (at school or home) and describe the extent to which it provides literature...

See similar textbooks

Similar questions

Calculate the total current , total resistance, and the Power across on each component using: FIRST APPROXIMATION SECOND APPROXIMATION THIRD APPROXIMATION
Q2/ If you want to measure a current of value 5 Ampere and the tolerance 0.1 Ampere find:- a) Percentage error b) Relative error
how get computed values with these
Which of the following is an accurate statement? A Any principal node can be used as reference node. B The potential between two principal nodes is zero. C) The principal node is considered as lower potential with respect to reference node. D There could be only one reference node in a given network.
Explain in sentence what is meant by effective current and effective voltage.
How is the concept of duality employed in the design and analysis of electrical circuits?
Subject:Circuits INote:Support the problems with circuit diagram and label the pertinent partsPlease with full solution
3) Calculate the resistance of a cross-sectional ared A Qd mm) and resistivityof(50* Fl the wire is drawn out to three times its original length, times would the resistance increave ? (100m) wire having a How many [500m, 9 times]
A. Find a11. Express your answer using three significant figures. B. Find a12 . Express your answer using three significant figures and include the appropriate units C. Find a21 . Express your answer using three significant figures and include the appropriate units D. Find a22 . Express your answer using three significant figures and include the appropriate units
Question 4 (a) A PMMC movement with a coil resistance of 25 0 requires 0.8 mA for full scale deflection. Specify: a. The coil voltage required for full scale deflection. b. The shunt resistance required for a 0-1 A ammeter. c. The multiplier resistance required for a 0-10V voltmeter. d. Draw both instruments.
choose the correct answer