Recent content by kioria

1. The problem Show that \int^{1}_{0}x^{m}(1-x)^{n} dx = \frac{m!n!}{(m+n+1)!} for all integers m, n \geq 0 The question is under "Reduction" topic, so I assume we solve this via reduction. 2. My attempt My attempt is as follows: Let x = cos^{2}x Then we get \frac{1}{2}\int...

Cheers

Hi, Given the function: P_{k} = \frac{20}{5^{k}} for k \geq 2 How would you prove that P is a probability distribution? I would think that you prove that P is bounded by 0 and 1 (i.e., 0 \leq \Sigma P_{k} \geq 1) And I guess the leading question is how you would prove that a function...

Thanks AKG, its very clear.

The C_{k} tends to increase dramatically as the input changes, say from well sorted array to totally reversed array. For example: A_{1} = {1,2,7,3,4,5,6} : C = 4 B_{3} = {1,6,5,4,2,3,7} : C = 9, that is almost double the number of swaps. What accounts for these? (Unless I totally...

Ok I'm going to need some time for this. Will post back if I can't reason it. First paragraph seems understandable - rest I'll give it a try. Thanks.

In the problems below A[1, ..., n] denotes an array consisting of arbitrary n real numbers, and A[j] denotes the element in the j-th place of the array A[1, ..., n]. 1) Let k be a fixed natural number. Consider the family A_{k} of all arrays A[1, ..., n] satisfying that for every i ≤ n there...

In the problems below A[1, ..., n] denotes an array consisting of arbitrary n real numbers, and A[j] denotes the element in the j-th place of the array A[1, ..., n]. 1) Let k be a fixed natural number. Consider the family A_{k} of all arrays A[1, ..., n] satisfying that for every i ≤ n there...

Ahhh I see it now. So k acts to restrict the cardinality of the set S in relation to the final answer. Since you start off with \frac{n}_{n} which is probability of an accident happening on any of the n days, as days go by you can only have accidents if k is sufficiently big enough for n...

I see what you mean there... [EDIT] But shouldn't the choice be chosen from total number of accidents that have happened over the period of n days? :uhh:

I believe the question says: N = \{k_1, k_2, ... k_n\} where n is an Integer for n days. Let k denote k_1 + k_2 + ... + k_n. I am puzzled as to why \frac{(n - k)}_{n} is omitted. I can't seem to picture the relationship between the final result and k.

Perhaps, P(A) = the probability of accident happening on first day AND the probability of accident happening on second day AND ... AND the probability of accident happening on the last day. This turns out to be: P(A) = \frac{n(n-1)...(n-k+1)}_{n^k}, since only 1 accident per days needs to...

This is a simple example in a textbook, I haven't done probability since High school and probability being all too confusing... I cannot seem to overcome this problem. Here's the problem: a) Assume k car accidents occurred in n days. Assume that accidents are equally likely on any day. Let A...

I messed up with my x's and N's, the top line should really be f(N). I am having trouble finding g(N) and the constant value C.

I have been given an assignment, a small one, which simply takes in number of points in cartesian coordinate format: (x, y) - then - the assignment specified that the program needed to calculate distances of every permutation possible - then return with the set(s) of points that had the shortest...