hw4sol_fall03

# hw4sol_fall03 - AMS 310.01 Fall 2003 4.30 Homework 4...

This preview shows pages 1–2. Sign up to view the full content.

AMS 310.01 Fall 2003 Homework 4 Solutions 4.30 (a) The mean µ is given by 0(0.4) 1(0.3) 2(0.2) 3(0.1) 1 μ = + + + = (b) The variance 2 σ is given by 2 2 2 2 2 (0 1) (0.4) (1 1) (0.3) (2 1) (0.2) (3 1) (0.1) 1 σ = - + - + - + - = 4.34 Using the formula, 0 1 ( 1) 2 n i i n n = = + and 2 0 1 ( 1)(2 1) 6 n i i n n n = = + + We find 0 1 1 2 n i n i n μ = + = = , and 2 2 2 2 2 1 1 ( 1) ( 1)( 1) ( 1) ' ( 1)(2 1) [ ] 6 2 12 12 n n n n n n n n σ μ μ + + - - = - = + + - = = 4.36 (a) The mean µ is given by 5 . 2 32 1 5 32 5 4 32 10 3 32 10 2 32 5 1 32 1 0 = + + + + + = μ (b) 5 . 2 ) 5 (. 5 = = = p n μ 4.40 (a) The probabilities are : 4 4 0 3 4 ( 0) 8 56 3 P X ���� ���� ���� = = = �� �� �� , 4 4 1 2 24 ( 1) 8 56 3 P X ���� ���� ���� = = = �� �� �� 4 4 2 1 24 ( 2) 8 56 3 P X ���� ���� ���� = = = �� �� �� , 4 4 3 0 4 ( 3) 8 56 3 P X ���� ���� ���� = = = �� �� �� Thus, 4 24 24 4 0 1 2 3 1.5 56 56 56 56 μ = + + + = 2 2 2 2 2 4 24 24 4 30 (0 1.5) (1 1.5) (2 1.5) (3 1.5) 0.5357 56 56 56 56 56 σ = - + - + - + - = = (b) From the Special formulas, we have 4 3 1.5 8 a n N μ = = = , 2 2 2 ( )( ) 3 4 4 5 240 0.5357 ( 1) 8 7 448 n a N a N n N N σ - - ��� = = = = -

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

View Full Document
4.42 The tail probabilities and upper bounds are Number of sd’s Upper Bound of tail probabilities Tail probabilities from binomial (16; 1/2) 1 1 0.4544 2 1/4 0.0768 3 1/9 0.0042 The upper bound of the tail probability comes from 2 1 (| | ) P X k k μ σ - where k is the number of standard deviations. An example of the calculation of the tail probabilities for the binomial distribution with
This is the end of the preview. Sign up to access the rest of the document.

{[ snackBarMessage ]}

### What students are saying

• As a current student on this bumpy collegiate pathway, I stumbled upon Course Hero, where I can find study resources for nearly all my courses, get online help from tutors 24/7, and even share my old projects, papers, and lecture notes with other students.

Kiran Temple University Fox School of Business ‘17, Course Hero Intern

• I cannot even describe how much Course Hero helped me this summer. It’s truly become something I can always rely on and help me. In the end, I was not only able to survive summer classes, but I was able to thrive thanks to Course Hero.

Dana University of Pennsylvania ‘17, Course Hero Intern

• The ability to access any university’s resources through Course Hero proved invaluable in my case. I was behind on Tulane coursework and actually used UCLA’s materials to help me move forward and get everything together on time.

Jill Tulane University ‘16, Course Hero Intern