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Homework Assignment
Due Date: September 23, 2005
Please keep in mind the statement in the syllabus concerning homework assignments: "Students may consult with the lecturer (and are encouraged to do so) for help on these problems but they may not consult with each other." Copying homework is considered a form of academic cheating and will be treated as such!
1. Factorial. (2 points)
a) Evaluate 2005!. Express your answer first as a power of e (the base of the natural logarithms) and then as a power of ten. Please use at least seven significant figures in your responses. b) If the above number were to be written in fixed point notation what would be the first digit and how many digits long would it be?
2. Distributions! (5 points)
Suppose a container contained 40 particles. a) What is the probability that 12 of the particles are one fifth of the container? b) In how many ways could 12 particles be in one fifth of the container? c) What is the probability that 30 of the particles are one fifth of the container? d) In how many ways could 30 particles be in one fifth of the container? e) What is the average number of particles in one fifth of the container?
2. Gaussian Probability. (3 points)
A certain system is described by the Gaussian distribution function with = 10,000 and σ = 200. a) What is P(10,000)? b) What is P(10,050)?
Homework Assignment
Due Date: September 23, 2005
Please keep in mind the statement in the syllabus concerning homework assignments: "Students may consult with the lecturer (and are encouraged to do so) for help on these problems but they may not consult with each other." Copying homework is considered a form of academic cheating and will be treated as such!
1. Factorial. (2 points)
a) Evaluate 2005!. Express your answer first as a power of e (the base of the natural logarithms) and then as a power of ten. Please use at least seven significant figures in your responses. b) If the above number were to be written in fixed point notation what would be the first digit and how many digits long would it be?
2. Distributions! (5 points)
Suppose a container contained 40 particles. a) What is the probability that 12 of the particles are one fifth of the container? b) In how many ways could 12 particles be in one fifth of the container? c) What is the probability that 30 of the particles are one fifth of the container? d) In how many ways could 30 particles be in one fifth of the container? e) What is the average number of particles in one fifth of the container?
2. Gaussian Probability. (3 points)
A certain system is described by the Gaussian distribution function with = 10,000 and σ = 200. a) What is P(10,000)? b) What is P(10,050)?
Homework Assignment
Due Date: September 23, 2005
Please keep in mind the statement in the syllabus concerning homework assignments: "Students may consult with the lecturer (and are encouraged to do so) for help on these problems but they may not consult with each other." Copying homework is considered a form of academic cheating and will be treated as such!
1. Factorial. (2 points)
a) Evaluate 2005!. Express your answer first as a power of e (the base of the natural logarithms) and then as a power of ten. Please use at least seven significant figures in your responses. b) If the above number were to be written in fixed point notation what would be the first digit and how many digits long would it be?
2. Distributions! (5 points)
Suppose a container contained 40 particles. a) What is the probability that 12 of the particles are one fifth of the container? b) In how many ways could 12 particles be in one fifth of the container? c) What is the probability that 30 of the particles are one fifth of the container? d) In how many ways could 30 particles be in one fifth of the container? e) What is the average number of particles in one fifth of the container?
2. Gaussian Probability. (3 points)
A certain system is described by the Gaussian distribution function with = 10,000 and σ = 200. a) What is P(10,000)? b) What is P(10,050)?
Homework Assignment
Due Date: September 23, 2005
Please keep in mind the statement in the syllabus concerning homework assignments: "Students may consult with the lecturer (and are encouraged to do so) for help on these problems but they may not consult with each other." Copying homework is considered a form of academic cheating and will be treated as such!
1. Factorial. (2 points)
a) Evaluate 2005!. Express your answer first as a power of e (the base of the natural logarithms) and then as a power of ten. Please use at least seven significant figures in your responses. b) If the above number were to be written in fixed point notation what would be the first digit and how many digits long would it be?
2. Distributions! (5 points)
Suppose a container contained 40 particles. a) What is the probability that 12 of the particles are one fifth of the container? b) In how many ways could 12 particles be in one fifth of the container? c) What is the probability that 30 of the particles are one fifth of the container? d) In how many ways could 30 particles be in one fifth of the container? e) What is the average number of particles in one fifth of the container?
2. Gaussian Probability. (3 points)
A certain system is described by the Gaussian distribution function with = 10,000 and σ = 200. a) What is P(10,000)? b) What is P(10,050)?
