HW5sol - Homework 5 Probability Plots Two/More R.V.S...

Info iconThis preview shows pages 1–3. Sign up to view the full content.

View Full Document Right Arrow Icon

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full Document Right Arrow Icon
This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: Homework 5 Probability Plots, Two/More R.V.S., Sampling, Estimation The question numbers are from 5 th edition Page 1 Probability Plots: Question 1 6-74 Construct a normal probability plot of the insulating fluid break down time data in Exercise 6-8. Does it seem reasonable to assume that breakdown time is normally distributed? (Data: 0.19, 0.78, .96, 1.31, 2.78, 3.16, 4.15, 4.67, 4.85 ) Answer: It appears that the data do not come from a normal distribution. Very few of the data points fall on the line. Two or More Random Variables Question 2 5-15 Determine the value of c that makes the function f(x,y)=cxy a joint probability density function over the range 0<x<3 and 0 <y<x. Determine the following: (a) P(X<1,Y<2) (b) P(1<X<2) (c) P(Y>1) (d) P(X<2, Y<2) (e) E(X) (f) E(Y) (g) Marginal probability distribution of X (h) Conditional probability distribution of Y given that X = 1 (i) E(Y|X=1) (j) P(Y>2|X=1) -40-20 20 40 60 1 5 10 20 30 40 50 60 70 80 90 95 99 Data Percent Exercise 6-2 Data Normal Probability Plot for time Mean StDev 14.3589 18.3769 ML Estimates Homework 5 Probability Plots, Two/More R.V.S., Sampling, Estimation The question numbers are from 5 th edition Page 2 (k) Conditional probability distribution of X given that Y = 2 Answer : . 8 81 8 2 2 3 3 4 3 3 2 c x dx x c dx y x c x xydyd c x x ∫ ∫ ∫ ∫ = = = Therefore, c = 8/81 a) P(X<1,Y<2)= . 81 1 8 1 81 8 2 81 8 81 8 1 1 3 = = = ∫ ∫ ∫ dx x x xydyd x b) P(1<X<2) = ....
View Full Document

{[ snackBarMessage ]}

Page1 / 7

HW5sol - Homework 5 Probability Plots Two/More R.V.S...

This preview shows document pages 1 - 3. Sign up to view the full document.

View Full Document Right Arrow Icon
Ask a homework question - tutors are online