Solving a Recurrence Relation

Solve the following recurrence relation: a(n) = a(n-1) + 3(n-1), a(0) = 1 I know this should not be a difficult problem, but my main problem is in solving the problem when the coefficient of the a(n-1) term is 1. Also, when a summation is in the solution, I do not understand how to convert from a summation to a ...continues

Angles and matrices

Project 3 2. Lance Armstrong won the 2003 Tour de France. The wheel on his bike had a 63 inch diameter. His average speed was 40 km / hour. What was the angular speed of the wheel in revolutions per hour? 3. A construction company is making picnic pavilions where the roof will be supported by two sets of beams. The bea ...continues

Vectors, graphs, and counting

Project 4A 1. Explain why vectors QR and RQ are not equivalent. 2. Explain in your own words when the elimination method for solving a system of equations is preferable to the substitution method. 1. In Washington DC, there is a large grassy area south of the White House known as the Ellipse. It is actually an ellipse wi ...continues

Subsequence

In a line of people you are looking for a subsequence of 4 (not necessarily consecutive = neighboring) people with increasing height. How many people should be in the line so that you can be sure to find this subsequence?

Induction Proof

see attachment.

probability that a 2x2 matrix of numbers chosen from a set has a det of zero

see attatched...

Maximizing the expected amount of money and maximizing the expected amount of commodity

#23. You have $1000 and a certain commodity presently sells for $2 per ounce. Suppose that after one week the commodity will sell for either $1 or $4 an ounce, with these two probabilities being equally likely. (a) If your objective is to maximize the expected amount of money that you possess at the end of the week, what stra ...continues

If someone buys 3 packages, what is the probability that he or she will return exactly one of them?

# 48. It is known that diskettes produced by a certain company will be defective with probability 0.01, independently of each other. The company sells the diskettes in packages of size 10 and offers a money-back guarantee that at most 1 of 10 diskettes in the package will be defective. If someone buys 3 packages, what is the pro ...continues

Probability density function

# 3. Consider the function f (x) = C ( 2x - x³) 0 < x < 5/2 f (x) = 0 otherwise. Could f be a probability density function? If so, determine C. Repeat if f (x) were given by f (x) = C ( 2x - x²) 0 < x < 5/2 f (x) = 0 otherwise.

The problem is from probability class.

#4. The probability density function of X, the lifetime of a certain type of electronic device (measured in hours), is given by f (x) = 10/x2 x > 10 f (x) = 0 x ≤ 10 (a) Find P{X > 20}. (b) What is cumulative distribution function of X? .. (see attachment)