# Tagged Questions

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### Writing probability as log

I have a question regarding the log probability and I am confused on this. The question is: $$\hat P^{(t)}(x)=\sum_{i=1}^N v_i^{(t)}P_i^{(t)}(x)$$ which is some function of size $N$. The question ...
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### Discrete Random Variables Help in Understanding

A company wants to form a team of 6 employees. Suppose that 60% of all staff available for selection are male, and that all team members are selected at random. Let X be the random variable for ...
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### Combination Problem with Sofa [closed]

Suppose we have 5 sofa on room A. in this room, 4 students seated on these sofa. These Strudents go to another room for eating dinner, and after that come back to room A. how many way the students can ...
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### Expected value over many trials

I am a poker player and was talking to my friend about expected value. He claimed that if you play far enough above your bankroll, expected value can be negative, even if you have a skill edge. I ...
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### Problematic Permutation Problem

i see a problem without any definition. would you please help me? i want to calculate the number of permutations of 1,2,...,1392 that 696 numbers be in the natural positions (from all numbers, 696 ...
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### Alternatives to absolute error?

Let me explain my scenario in which I need to calculate absolute error. Lets say the X is the actual value. And X' is the value of X with some error 'e'. So X' = X + e'. Lets say i = 1 to 10000. I ...
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### DNA Sequence Distinct Way

we know The genetic code is based on the four nucleotides adenine (A), cytosine (C), guanine (G), and thymine (T). These are connected in long strings to form DNA molecule. with three A, one C, two G ...
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### 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. ...
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### 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 ...
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### 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 ...
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### 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?
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### 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 ...
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### 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 ...
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### 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 ...
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### 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 ...
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### 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 ...
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### 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 ...
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### 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 ...
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### 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 ...
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### 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 ...
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### 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 ...
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### 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? ...
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### 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 ...
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### 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 ...
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### 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: ...
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### 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 ...
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### 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.
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### 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 ...
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### 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 ...
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### 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 ...
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### 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) ...
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### 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 ...
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### 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 $P[head>\frac{n}2 + k\sqrt{n}]$ < $e^{-{k^2/2}}$, ...
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### 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 $n$ ...
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### 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 ...
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### 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, ...
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### 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.
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### 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 ...
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### 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 ...
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### 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 ...
### 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 ...