0
votes
0answers
50 views

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 ...
0
votes
1answer
20 views

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 ...
0
votes
1answer
65 views

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 ...
1
vote
1answer
74 views

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 ...
1
vote
3answers
33 views

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 ...
1
vote
1answer
27 views

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 ...
0
votes
3answers
32 views

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 ...
2
votes
2answers
68 views

Constructing a function similar to x^3 between [0,1]

I'm trying to construct a function $f$, in order to normalize a dataset(obviously where all the element come from $[0,1] \in \mathbb{R}$. The big picture is that the envisioned $f: [0,1] \rightarrow ...
0
votes
1answer
33 views

Cross-Validation

Does anyone understand the paragraph below? The paragraph comes from Cross-valiation explanation at wikipedia. "It can be shown under mild assumptions that the expected value of the MSE for the ...
1
vote
2answers
27 views

Ball Probability help

A bowl contains 5 red balls, 3 white balls and 2 blue balls. Two balls are seleceted at random from the bowl (without replacement). A) What is the probability that both are red? which is 2/9 B) What ...
1
vote
1answer
77 views

Card probability

There are two 10-card decks, consisting of 5 red cards and 5 blue cards each. Both are shuffled separately. One card is then dealt from each deck and compared. This is repeated for all 10 pairs of ...
0
votes
1answer
46 views

How to come up with a probability distribution knowing the mean value? [closed]

I would like to know about some algorithms or techniques to find a discrete probability distribution knowing the mean value. Let's say given the mean=2.5. The probability distribution can be $x_1=2, ...
0
votes
0answers
53 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
379 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 ...
5
votes
0answers
52 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
95 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, ...
-3
votes
1answer
70 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
39 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
72 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
9 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
482 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
84 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
138 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
75 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
25 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
151 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
37 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 ...
2
votes
1answer
44 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
94 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
38 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
94 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
78 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
26 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
118 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
50 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
103 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
50 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
82 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
2answers
47 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
67 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
205 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 $P[head>\frac{n}2 + k\sqrt{n}]$ < $e^{-{k^2/2}}$, ...
1
vote
1answer
503 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
153 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 ...
1
vote
1answer
36 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
49 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
246 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
44 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 ...