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

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

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