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Answers to Selected Exercises - MATEMATIKA INTÉZET

Answers to Selected Exercises4. Special Normal Gamma Chi Square Student t F Multivariate Normal Beta Weibull Zeta Pareto Logistic Lognormal Extreme Value 's Introduction f (x) =1b exp( x ab), x >a f (x) =1 b (1+x ab)2, x 2. The Normal Distribution Let X denote the volume of beer in liters (X > ) = Let X denote the radius of the rod and Y the radius of the hole. (Y X < 0) = Let X denote the combined weight of the 5 peaches, in ounces. (X > 45)= The Gamma Distribution (X > 3) =172 e 3 , Q2= , Q3= , Q3 Q1= , , Q2= , Q3= , Q3 Q1= , , Q2= , Q3= , Q3 Q1= , c.

Answers to Selected Exercises 4. Special Distributions 1. Introduction 2. The Normal Distribution 3. The Gamma Distribution 4. The Chi Square Distribution

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Transcription of Answers to Selected Exercises - MATEMATIKA INTÉZET

1 Answers to Selected Exercises4. Special Normal Gamma Chi Square Student t F Multivariate Normal Beta Weibull Zeta Pareto Logistic Lognormal Extreme Value 's Introduction f (x) =1b exp( x ab), x >a f (x) =1 b (1+x ab)2, x 2. The Normal Distribution Let X denote the volume of beer in liters (X > ) = Let X denote the radius of the rod and Y the radius of the hole. (Y X < 0) = Let X denote the combined weight of the 5 peaches, in ounces. (X > 45)= The Gamma Distribution (X > 3) =172 e 3 , Q2= , Q3= , Q3 Q1= , , Q2= , Q3= , Q3 Q1= , , Q2= , Q3= , Q3 Q1= , c.

2 Let X denote the petal length in centimeters. (X) = (X)= 2b. Let X denote the lifetime in hours. (X > 300) = 13 e 3 (X) = (X)= 200c. (18 < X < 25)= , (18 < X < 25) , y80 The Chi-Square Distribution , Q2= , Q3= , Q3 Q1= , , Q2= , Q3= , Q3 Q1= , , Q2= , Q3= , Q3 Q1= , , Q2= , Q3= , Q3 Q1= , d. Let Z denote the distance from the missile to the target. (Z < 20) = 1 e 2 (15 < X < 20)= , (15 < X < 20) , The Student t Distribution 1, Q2= 0, Q3= 1, Q3 Q1= 2, , Q2= 0, Q3= , Q3 Q1= , , Q2= 0, Q3= , Q3 Q1= , , Q2= 0, Q3= , Q3 Q1= , d. ( <T < ) = , ( <T < ) , The F distribution , Q2= 1, Q3= , Q3 Q1= , , Q2= 932, Q3= , Q3 Q1= , , Q2= , Q3= , Q3 Q1= , , Q2= 1, Q3= , Q3 Q1= , The Beta Distribution , Q2= , Q3= , Q3 Q1= , , Q2= , Q3= , Q3 Q1= , , Q2= , Q3= , Q3 Q1= , , Q2= , Q3= , Q3 Q1= , , Q2= , Q3= , Q3 Q1= , , Q2= , Q3= , Q3 Q1= , The Weibull Distribution Q1= , Q2= , Q3= , Q3 Q1= , (T > 1500)= (T) = , sd(T)= (t) = The Zeta Distribution (X > 4) = 1 496 2 (X) = (X)= The Pareto Distribution Q1= , Q2= , Q3= , Q3 Q1= Let X denote income.

3 (2000 < X < 4000) = so the proportion is , Q3= , Q3 Q1= (X) = (X)= 1( )= The Logistic Distribution ( 1 < X < 2) = Q1= , Q2= 0, Q3= , Q3 Q1= F 1( )= , F 1( )= The Lognormal Distribution (X > 20) = Q1= , Q2= 1, Q3= , Q3 Q1= (X) =e52 (X)= e6 e5 Benford's Law (y) = y for y 1101[ ), .a. (Y) = , var(Y) = ,b. (N1=n)1 (N1) = , var(N1) = (N1=n1, N2=n2)n2 \n11234567890 (N2=n)0 (N2) = , var(N2) = Laboratories > 4.]

4 Special Distributions > Answers to Selected Exercises


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