Homework Statement
Let the independent random variables X1,X2,X3 have the same cdf F(x). Let Y be the middle value of X1,X2,X3. Determine the cdf of Y.
Homework Equations
F(x) = P(X<=x) = ∫-inf to x f(y)dy
The Attempt at a Solution
I don't understand the question, what does it...
Homework Statement
A gas supply company is trying to set up contracts with two clients, A and B. The company will make a profit of ten million dollars for each contract that is successfully agreed. The probability of agreeing a deal with client A is 1/4 and the probability of agreeing a deal...
The class is known as Advanced Discrete Structures, crosslisted with Mathematics and Computer Science. Apparently we cover topics of both formal logic and abstract computer science.
This is the notes we got from the professor. Maybe this would be of help...
Homework Statement
Prove by finite list induction
∀xs:: [a]. map (\x -> x) xs = xs
Homework Equations
map f [ ] = [ ]
map f (x : xs) = (f x) : map f xs
The Attempt at a Solution
The list induction principle to prove a finite lists of type a is
[P([ ])^
∀x :: a. ∀xs ...
Homework Statement
x^4 + 3x^3 - 7x^2 - 15x + 18 = 0
Find x
Homework Equations
First Derivative?
Second Derivative?
The Attempt at a Solution
Normally, I'd use Ferrari's method to tackle this problem but I am required to use derivation to find the answer...
Where do I go from here? Do...
Homework Statement
Find the limit of
\frac{x^3-2x^2-9}{x^2-2x-3}
as x->3
Homework Equations
The Attempt at a Solution
You factor the bottom portion and top portion, then it looks something like this
\frac{x(x^2-2x)-9}{(x-3)(x+1)}
I feel like I can go further about eliminating the...
Just so that I understand, why is it that the cylindrical shell method must be applied here? I was taught that when finding a volume revolved around X or Y axis, the above equation works well except you just have to be careful when you plug in for X or Y.
Homework Statement
The region bounded by y=e^-x^2, y=0, x=0 and x=1 is revolved around the y-axis. Find the volume.
Homework Equations
V = \int_{a}^{b} R^2 dy
The Attempt at a Solution
We must first express x in terms of y. So we get
\ln y = -x^2
x^2 = -\ln y
We substitute this to the...
Homework Statement
1.
f(n) = n - 100
g(n) = n - 200
2.
f(n) = log(2n)
g(n) = log(3n)
n >= 0 in all cases
Find out if f(n) is an upperbound, lowerbound or both of g(n)
Homework Equations
The Attempt at a Solution
in case of 1, f(n) has to be an upperbound of g(n) because...
Homework Statement
Show that the first three non-zero terms in the series expansion of (1-1/n)^1/n in ascending powers of 1/n are 1-(1/n)^2-1/2(1-n)^3 and find the term in (1/n)^4
Homework Equations
Macclaurin? Taylor?
The Attempt at a Solution
Can someone please point me on...
Then that simply means
f(b-1) = 1
f(b+1) = 1
So we have
1 = (b-1)^2 - 4(b-1) + a
1 = (b+1)^2 - 4(b+1) + a
0 = (b-1)^2 - 4(b-1) - (b+1)^2 + 4(b+1)
0 = (b-1)^2 - (b+1)^2 + 8
b = 2
Then,
1 = (2+1)^2 - 4(2+1) + a
1 = 9 - 12+ a
a = 4
a + b = 6 is what I get, but...
I understood why the discontinuity occurs, since |x-b|^n of n to the infinity could take you to 0 or a huge value (I think it was related to geometrical sum) depending on whether it's smaller than 1 or bigger than 1. I still do not have a clue how to get the specific values of a and b from it...
Homework Statement
f(x) = x^2 - 4x + a
g(x) = \lim_{n\rightarrow\infty} \frac {2|x-b|^n + 1}{|x-b|^n + 1}
let h(x) = f(x)g(x)
Find the sum of a+b that makes h(x) continuous for all x.
Homework Equations
Power Series??? Derivation to test continuity???
The Attempt at a Solution...
Ok, it's situation like these latex seriously does a commendable job of pissing me off. How would you write the summation of index starting from j = 1 until n?
Homework Statement
When a conventional apging system transmits a message, the probability that the message will be received by the pager it is sent to is p. To be confident that a message is received at least once, a system transmits the message n times.
Assuming p = 0.8, what is the...
oh ok, then the next event is {FFS] so it's (1-p)^2 * p for the third attempt.
Ok, then the total probability is p + p(1-p) + p(1-p)^2
So I set this expression equal to 0.95 and solve for p?
Ok. Obviously, the probability of getting the ticket on the first call is p.
Probability on the second one is 1-(1-p)^2 and the third one is 1-(1-p)^3
Then the total probability is p + (1-(1-p)^2) + (1-(1-p)^3)
Am I right? And from this, do I set the whole equation to 0.95 and solve for...
Homework Statement
You are a manager of ticket agency that sells concert tickets. You assume that people will call 3 times in an attempt to buy the ticket and give up. You want to make sure that you are able to serve at least 95% of the people who wants tickets. Let p be the probability that a...
Homework Statement
Prove
a \times (b \times c) = (a * c)b - (a*b)c
For orthagonal coordinates, a,b,c
Homework Equations
Cross Product and Dot Product
The Attempt at a Solution
I thought about expanding both sides out and proving they are equal, but I just realized that the...
Welcome to PF, paretoptimal!
There is a specific method to take the antiderivative of the function you've shown. Have you studied integration by parts?
If no, I suggest you first read the following article to understand what it is.
http://en.wikipedia.org/wiki/Integration_by_parts
If...
That's what I was thinking, except that the series is multiplied by an exponential term (with n). And sorry, there was a mistake - there shouldn't be n in the final answer.