0
votes
0answers
25 views

Extension to the Coupon Collector Problem

If there's n different coupons. Instead of ordering coupons one-by-one until you collect all n coupons as in the traditional 'Coupon Collector Problem', what if the coupons came in packs of m coupons. ...
3
votes
2answers
347 views

What is the probability that $x_1+x_2+…+x_n \le n$?

Given that $X_1, X_2...$ are mutually independent random variables. For each $i$ with $1\le i \le n$ the variable $X_i$ is equal to either $0$ or $n+1$ $E(X_i)$ = $1$ also.. if $X_i$ is equal to ...
4
votes
0answers
44 views

Decrease of entropy when iterating a random discrete function

Let $m$ be a positive integer. Let $S$ be the set of non-negative integers $x$ less than $m$, with $|S|=m$. Let $X_0$ be the discrete uniform distribution over $S$, with $P(x)=\begin{cases} 1/m & ...
0
votes
2answers
58 views

part a) How many strings in the letters a, b, and c have length 10 and exactly four a's?

I did 10 choose 4 and that is 210 different ways for a to be arranged in length of 10, but I'm confused on the rest? FIGURED OUT PART A, not part B yet part b) How many strings in the letters a, b, ...
-1
votes
1answer
50 views

Independent Probability Events?

Events $A$ and $B$ in probability space $S$ are independent if the occurrence of one of them does not influence the occurrence of the other. In other words, $B$ is independent of $A$ if $P(B) = ...
0
votes
1answer
24 views

probability equiprobable space?

For the problem below are we going to use the equiprobable space. Which is In particular, if S contains n points then the probability of each point is 1/n . For an event A, P(A) = number of elements ...
2
votes
1answer
36 views

How to calculate the Lambda of Poisson distribution from mean of inter arrival time?

I have inter arrival time into a system mean equal to$ 0.45.$ Does $\lambda = \frac{1}{0.45}$ if I need to select Poisson as an arrival distribution?
0
votes
0answers
8 views

Predict values of some numerical vectors by using other numerical vectors with all these vectors in the same vector set

I need to solve a problem about predicting values of some numerical vectors by using other numerical vectors with all these vectors in the same vector set, which is generated by one or more black box ...
0
votes
3answers
184 views

A bowl contains 10 red balls and 10 blue balls, A women selects ball at random without looking?

How can we solve this question ? A bowl contains $10$ red balls and $10$ blue balls, and a women picks up balls from the bowl, at random, without looking. A) How many balls must she pickup in ...
0
votes
0answers
33 views

Calculate number of combinations & permutations for job assignment to machines

There are 12 machines (M). Each machine can execute for 20 slot (S) of time per session. We have 8 jobs (J) to be done. Each job requires 2 continuous slots (T). There is a fixed timeframe between the ...
1
vote
2answers
116 views

Statistics-Math-Probability

An urn is filled with 10 green balls, 4 red balls, and 2 orange balls. Three balls are selected without replacement. Calculate the following probabilities: (a) P(at least one ball is red) I think ...
2
votes
1answer
48 views

Differentiation for least squares method?

Is there any reason that we use mathematical differentiation of least squares method for regression analysis? The theory say we use differentiation supposing the sum of errors is 0. I I don't really ...
1
vote
0answers
18 views

How to find a function that can approximate another blackbox function programmaticly?

This question has been posted on http://stackoverflow.com/questions/21758016/how-to-find-a-function-that-can-approximate-another-blackbox-function-programmat I was suggested to post it here. I ...
1
vote
2answers
118 views

combination and permutation !!!!

I have 3 questions that i had a try to do but i didn't understand them could anybody please help me to solve these questions. For Q1 i know how to use the multiplication counting procedures for a) i ...
0
votes
1answer
33 views

Empirical formula of coverage probability

Can someone explain me how this formula calculates the coverage probability. Suppose I have a time series of size $n$. Then I can fit a model to this series and get its one-step ahead forecast and ...
1
vote
1answer
34 views

Extracting a ball from an urn, introducing it into the second. Expected value=?

We have two urns, the first with 6 white balls and 7 black balls and the second with 10 white balls and 5 black balls. We extract a ball from the first urn and introduce it into the second one, then ...
0
votes
1answer
67 views

Calculating probability of winning Power Ball

Today I tried to calculate the probability of winning a jackpot in Power Ball California Lottery. There are 1-59 numbers from which you have to guess 5 out of 5 and 1-35 numbers from which you have to ...
0
votes
1answer
23 views

How to know when to divide stem and leafs into two parts?

By two parts I mean when each stem is divided into low and high. For example in this question, do I need to divide each stem into two parts? What are the rules? Also is it positive or negative skew? ...
2
votes
2answers
65 views

Lottery game question?

In a lottery, you must match all 6 numbers drawn at random from 1 to 40 without replacement to win the grand prize, 5 out of 6 numbers to win second prize, and 4 out of 6 numbers to win third. The ...
2
votes
3answers
68 views

combinatoric question - balls arrangement

In how many ways can you arrange 200 balls into 40 cells, such that the sum of balls in cells 1-20 is greater (not equal) the sum of balls in cells 21-40? So, the number of posibilities can be ...
1
vote
0answers
24 views

How to sum correlation, or, calculate correlation of disjointed variables

I'm trying to calculate the correlation of 2 array of variables, but the array is disjointed in the middle - but I'm trying to obtain one correlation coefficient See the excel file I uploaded: ...
0
votes
3answers
90 views

Are these events independent or dependent? (Check my work)

I'm studying for my exam, and unsure about my answers for these 3 practise questions: My answers are as follow: Q1) Independent, as can have HTH which satisfies B but not A. Q2) Dependent, as the ...
0
votes
2answers
44 views

How to get the lowest passing grade in normal distribution

$$ Pr[X\le a]=0.05 $$ $$ P[{Y\le {{a-64}\over 7.1}]} = 0.05 $$ I tried up to here but I don't know what to do now... Hint please.
0
votes
1answer
81 views

Expected probability of coin flips

I would appreciate help with my exam studying. A question asks: If we flip a coin 30 times, with every head winning 5 dollars and for every tail losing 4 dollars. What is the expected value $E(W)$ of ...
2
votes
1answer
47 views

Probability of Combinations which have different probabilties.

I cannot figure this out. The problem goes A boy has a bag filled with balls: 1 red 2 green 4 Blue 7 White A child plays a game in which he withdraws one ball, writes down its color, and then ...
1
vote
0answers
75 views

Inclusion/exclusion probability

I am having a really hard time understanding inclusion/exclusion for probability. For counting i understand the concept that if you take A + B and they have something in common you are counting that ...
0
votes
0answers
35 views

Fisher's exact test, very small sample size, RxC table, gave me bad result

I apply Fisher's exact test on very very small sample size. Each location in the table would have about 1 or 2 samples. The fisher's method has no room to enumerate the the tables, and returns me a ...
0
votes
2answers
43 views

Generating a random number of higher range

I had a discussion with my friend about writing a function (a computer program) which generates 9 values randomly using a random number generator which generates 4 values, i.e I have a PRNG rand(4) ...
3
votes
1answer
66 views

Regarding calculating the bias of coin with uncertainty

Suppose you have a coin that you flip $n$ times and the result have $m$ heads and $n-m$ tails. How accurate can you predict the bias of the coin to be $\frac m n$? I know that ...
2
votes
1answer
185 views

Regarding probability bound of flip coins

Suppose you flip a fair coin 10,000 time how can you characterize the distribution of the occurrence of head? From the textbook, it says that $P[head>\frac{n}2 + k\sqrt{n}]$ < $e^{-{k^2/2}}$, ...
0
votes
1answer
346 views

Solve the problem using linearity of expectation.

A building has $n$ floors numbered $1, 2, \cdots , n,$ plus a ground floor $G$. At the ground floor, $m$ people get on the elevator together, and each gets off at a uniformly random one of the $n$ ...
0
votes
2answers
140 views

Probability density/mass function

I am a bit confused as to the difference between the probability mass function and the probability density function for a distribution of discrete variables. I understand there would be no mass ...
0
votes
0answers
14 views

simple trend measure/score

I am looking for a very simple (potentially ‘parameterisable’) measure to determine the trend of a discrete time series where the measurements are not necessarily equidistant. The output of the ...
1
vote
1answer
34 views

Combinatorial Techniques: Putting two and two together

This is a $3$-part question. I got the first two parts, but could not get the third part (which uses the first two parts): Pick sequence of $8$ coins from sack of $40$ coins, containing $10$ pennies, ...
2
votes
2answers
48 views

New to generating functions - how do I get the function from the sequence defined by $a_n= n$ for $n\geqslant 0$?

I'm given: $a_n= n$ for $n \geqslant 0$. I'm quite good at recursive generating functions, but I haven't came across a simpler one like this, so I'm sure I'm just overlooking something really basic.
0
votes
2answers
222 views

What is the probability of these events?

Suppose that $4$% of the patients tested in a clinic are infected with avian influenza. Furthermore, suppose that when a blood test for avian influenza is given, $97$% of the patients infected with ...
2
votes
0answers
60 views

Consider a bipartite graph and Deduce that there exist infinitely many bipartite graphs

Consider a bipartite graph $G=(X \cup Y, E)$ with both sides of equal size; we let $n$ denote $|X|=|Y|$ We are also given an integer $d\ge 3$ and we wish each vertex in $X$ to be adjacent to at most ...
2
votes
1answer
35 views

Random variable and trying to find $E(N)$

Given $N = \text{random variable that counts the fraction of trials that are successful trials} = 12$ $N = S/12$ $S = \text{number of successful trials}$ $E(N)= ?$ i don't know how to find ...
1
vote
2answers
43 views

Is my answer to this combinatorics question correct? Counting the number of functions where $F(a) = F(b)$?

Let $A = \{a, b, c, d, e, f\}$ and $B = \{1, 2, 3, 4, 5\}$. How many functions $F$ from $A$ to $B$ are there such that $F(a) = F(b)$. I looked at it like this: If $F(a)$ and $F(b)$ are equal, that ...
8
votes
3answers
2k views

How would I figure out how many anagrams of mississippi don't contain the word psi?

I'm really confused how I'd calculate this. I know it's the number of permutations of mississippi minus the number of permutations that contain psi, but considering there's repetitions of those ...
1
vote
0answers
39 views

maximising the frequency of mode.

I have 4 numbers 5,5,3,1. Now I have the number 5, which I can distribute in any manner to ...
3
votes
1answer
85 views
1
vote
2answers
50 views

How would I determine the number of solutions for the sum of this number?

We're given the following equation: $$x_1 + x_2 + x_3 + x_4 + x_5 = 20$$ I know that the simple amount of solutions to this is $\binom{5+20-1}{5-1}$, but for the following questions I'm slightly ...
3
votes
3answers
75 views

I'm asked to give a combinatorial proof of the following question, how would I go about doing it?

The hint we're given is to think of it in terms of grid paths. I don't necessarily want the answer, I'm interested in learning how to do this. Could anyone offer an explanation (clearly please) on ...
0
votes
1answer
201 views

Gumbel distribution and expected values

Suppose that $V= max_i${$V_i+\epsilon_i $} where $i=1...N$ and each $epsilon_i$ has a a type 1 extreme value distribution with $F(x)=e^{e^{-x}}$ I need to show that $E[V]=u+ln(\sum_je^{V_j})$ ...
-3
votes
2answers
61 views

How would I find the number of solutions to equation

$x_1 + x_2 + x_3 + x_4 + x_5 = 20$ if $0\leq x_i\leq 5$ I know how to get the total amount without restrictions. $24C4 = 10 626$ But I'm not sure how I would do it if there's a restriction like ...
1
vote
2answers
37 views

How do i apply multinomial laws in this question?

the Question is i assume i have 15 students in class A grade obtain probaiblity = 0.3 B grade obtain probability =0.4 C grade obtain probability = 0.3 and I have this question What is the ...
1
vote
1answer
411 views

How do I find the number of bit strings with 3 consecutive 0s in a bit string of length n?

Say n is 8. How would I ever solve this problem? I've Googled around and searched this site but I haven't come up with much. I'm not even looking for the answer necessarily, just the process by ...
0
votes
0answers
59 views

Define a problem using chernoff bounds

We are preparing this for an exam. Given the division of a plane into a number of regions of different sizes. We would like to find, or guess, which is the biggest region, by doing the following. We ...
1
vote
1answer
854 views

What is the probability of two people meeting?

I am trying to figure out a solution to the following problem: Let there be two groups of people, Group A and Group B. Group A represents x percent (e.g. 1%) of the world's population, and Group B ...