0
votes
0answers
5 views

Determine a distribution of a gaussian stochastic at different time

I would like to determine the autocorrelation function of a Gaussian stochastic. Let see my problem So my solution is The distribution of $y=x(t_1)-x(t_2)$ is also a Gaussian stochastic with ...
1
vote
2answers
22 views

Probability between two dice games

Two games, both use un-biased 6 sided dice. game A, Sam throws one die 4 times. He wins if he rolls at least a 6 game B, he has 24 turns, and each time he rolls two dice simultaneously. He wins if ...
0
votes
1answer
58 views

Gambler's ruin and coin toss

Edit 3. Fixed question to be more clear and include current solution Problem Two players player 1 and player 2 plays a game of fair coin flipping. Player 1 starts with $A$ coins and Player 2 with ...
1
vote
1answer
26 views

raBinomial distribution with dependent trials?

I need your help with following problem: String with n characters is given. For each character in string there is probability p that it is wrong. Now you take a sliding window of length k, k<= n, ...
0
votes
0answers
24 views

Stat problem! Why is this? [duplicate]

This is a statistics problem. although this is not a problem which needs an answer, I want to know the reason Why this is right. Can you guys help me ? Thanks in advance!
-3
votes
1answer
90 views

How do you answer this Bayes theorem question? [closed]

Your computer is acting strangely and you suspect it has a virus. Unfortunately all 5 of your virus detection programs are outdated. If your computer has a virus then each program, independently of ...
0
votes
2answers
50 views

Probability/Set theory problem

The problem is: In some country, there are 3 newspapers. 20% of the population read newspaper A, 16% read B, and 14% read C. 8% of the population read both A and B, 5% read A and C, and 4% ...
1
vote
1answer
29 views

Proof of addition rule of probabilities with 4 events

I need to show that, given a event space and four events. If the only non-empty intersections between them are $A\cap B$, $B\cap C$, $C\cap D$, $D\cap A$, then: $P(A\cup B\cup C\cup ...
1
vote
0answers
56 views

Efficient calculation of minimal expected number of inversions

Problem: I have an array of size n with Z inversions initially and I am allowed to perform K operations where each operation can be decrease the number of inversions by 1. make a random shuffle of ...
0
votes
1answer
23 views

Ratios and probability mass function

It was given that $p_{2,3} = 2$ and $p_{0,1} = 12$ $p_{k, k+1} = \frac{P(X=k+1)}{P(X=k)}, k=0,1,2,...,n = (\frac{n-k}{k+1})(\frac{1-\theta}{\theta})$ The question was: Find $P(X \geq 2)$. Answer: ...
1
vote
0answers
13 views

Simple random walk conditioning on non-return

Consider a simple symmetric random walk on $\mathbb{Z}$, $(S_t)_{t \geq 0}$, with $S_0=0$. Let $P_{k,j}$ be the probability that the walker hits the point $k$ without returning to the origin in ...
2
votes
1answer
36 views

In how many ways you can put n white balls and 2n black balls into n boxes if at least one black ball have to be in each box

n - number of white balls 2n - number of black balls In how many ways you can put it into n boxes? It have to be at least one black ball in each box. My idea: First of all let's put one black ball ...
3
votes
4answers
56 views

Show $P\left(A-B\right)=P\left(A\right)-P\left(A \cap B \right)$

I'm trying to show that, given two events $A,B \in \Omega$ ($\Omega$ is a sample space): $$P\left(A-B\right)=P\left(A\right)-P\left(A \cap B \right)$$ I know $A-B = A \cap B^C$, but I don't know how ...
3
votes
0answers
36 views

A probability of a monochromatic cycle on a randomly colored lattice graph.

Let $G$ be an undirected $6 \times 6$ lattice graph. The $36$ vertices of $G$ are each randomly colored with one of $5$ colors with equal probability. Such a coloring is called "successful" if and ...
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
21 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
71 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 ...
0
votes
0answers
31 views

Problem calculating the average power of a vector?

I am calculating the average power of a vector. I would like to compare the final expression with the simulation. However, they are not equal. Please help me to point out which steps are wrong. Thank ...
1
vote
0answers
36 views

Linear model for data that follow gaussian distribution

I have a question about linear regression. We have the linear regression of input data $(X,Y)=((x_1,y_1),(x_2,y_2)...(x_n,y_n))$ is $$F=aX+b$$ a,b are factors of the linear line, $y_i$ is {-1,1}. ...
1
vote
1answer
79 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 ...
4
votes
1answer
41 views

Derive a procedure to select one of the 2 options with equal probability when we are not using a fair coin.

Derive a procedure to select one of the 2 options with equal probability when we are not using a fair coin. $P(\text{H}) = p$. $P(\text{T}) = 1 - p = q$. I came up with the following two-roll ...
0
votes
2answers
28 views

Reliability Probability problem

What is the Probability that at least one close path is formed from A to B where each switch has a Probability of close = p and each switch acts independent of the other Proposed Solution Let ...
1
vote
1answer
34 views

Probability of a certain result obtaioned by throwing an octahedron

Assume having a fair octahedron. We throw it $93$ times and get the following results: $\{33;7;8;1;2;0;5;37\}$ The numbers represent how many times the die fell on side $1, 2,...., 8$. What is the ...
0
votes
1answer
42 views

Unusual conditional probability problem

I came across this task in an exam a few days ago: There are 4 men. The first man receives a signal (a "YES" or a "NO"), and tells it to the second man, the second to the third and the third to the ...
1
vote
0answers
26 views

Convex Hull of discrete points

If i was to give an $n \times n$ grid with each grid point having probability $p$ of being selected, would it be difficult to calculate distributions of various measures regarding the convex hull of ...
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 ...
1
vote
1answer
47 views

Calculate Huffman code length having probability?

Having an alphabet made of 1024 symbols, we know that the rarest symbol has a probability of occurrence equal to 10^(-6). Now we want to code all the symbols with Huffman Coding. How many bits ...
0
votes
1answer
86 views

counting runs of empty bins

Here is a variation of balls and bins problem. Throwing $m$ balls uniformly and independently into $n$ bins labeled $0,1,2,\ldots,n-1$. Counting empty bins of run length $k$: There is a $k$-gap ...
0
votes
1answer
45 views

Probability Question on Urns and numbered balls

An urn contains $10$ balls numbered $1$ to $10$. A set of $3$ balls is drawn from the urn. Let $X$ record the largest number showing. Compute $P(X=7)$. I have to do this on excel. I'm assuming I ...
2
votes
1answer
67 views

k-Nearest nodes: Average distance between connected nodes when search radius is non-integer

Say I have an infinitely large grid where the probability any given square contains a node is $p$. Each node makes a connection with its $k$ nearest neighbours. How do I calculate the average ...
0
votes
1answer
30 views

Truth Tables. (If Q, then P)

Suppose people from Tracy always tell the truth and people from Livermore always lies, You meet Diego and he says,' If I came to San Jose on the train, then I am from Livermore ."is it possible ...
0
votes
1answer
24 views

Risk Faced With Insurance

I'm studying a simple models of insurance. Suppose that a machine breaks down with probability $p$, and suppose that an insurance company collects enough in premiums to pay for $k$ breakdowns. What ...
0
votes
0answers
309 views

How can I derive the PDF from conditional probabilities?

I have some function $P(i)$ which is the probability of success for an experiment on the $i$th trial. The probability mass function for the first successful trial is: $$PMF(n) = \left( ...
3
votes
2answers
94 views

why generating function $A(z) = 1 + z + z^2 + \cdots$ can be denoted as $\frac{1}{1-z}$

It is easy to see that $1 + z + z^2 + \cdots$ is equal to $\frac{1}{1-z}$ when $1 > z > 0$ and for $z >= 1$, they are not equivalent. So I have thought $\frac{1}{1-z}$ is just a short for the ...
1
vote
1answer
43 views
0
votes
0answers
16 views

Expected value of a function hat check n =3

Hat check experiment with 3 hats, six outcomes are 1,2,3 and then 2,1,3 and then 3,2,1 1,3,2 and then 2,3,1 and then 3,1,2 Z is income defined by 3 + 4N (N is how many ...
0
votes
2answers
58 views

Trying to understand a probability question

I'm trying to understand a probability question regarding a biased coin, not quite sure how to factor in the biased probability in the question, and also I wanted to make sure the answer is correct, ...
1
vote
1answer
40 views

Finding the variance of hat check experiment

This is the hat check experiment with 3 hats except the outcomes ${1,2,3}$ ${1,3,2}$ ${2,1,3}$ ${3,2,1}$ Have probability $1/5$ and the rest are $1/10$ I have to know the variance on N, which ...
-1
votes
1answer
61 views

finding the pattern [closed]

Hi Can Someone help me solve the below Back in the day men always wore hats and when they went to a club they would have a hat-check girl store their hats. If n men checked hats, in how many ...
0
votes
2answers
22 views

Probability help ball question

A bowl contains $5$ red balls, $3$ white, and $2$ blue balls. Two ball are selected without replacement. What is the probability that the two balls are a different colour? The answer that I got is ...
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 ...
0
votes
0answers
86 views

Expectation and Variance of a Discrete Uniform Distribution using the Probability Generating Function and Cumulant Generating Function

Hi I just derived the MGF of a discrete uniform distribution and found it to be: [e^t - e^t(m+1)]/(1 - e^t)m and the pgf is ...
1
vote
3answers
49 views

Flip a coin 3 times. What is the probability that number of tails is odd?

We flip a fair coin (independently) three times. Define the following events: A = "the number of tails is odd" B = "the number of heads is even" What is the probability of event A and event B?
0
votes
1answer
33 views

Flipping a fair coin 3 times. T/F

We flip a fair coin (independently) three times. De fine the following two events: A = "the number of tails is odd" B = "the number of heads is even" True or false: The events A and B are independent. ...
0
votes
1answer
59 views

Determine the probability that a randomly selected integer is divisible by one of several integers.

If you choose an element x uniformly at random from the set {1,2,...,100}, what is the probability that x is divisible by 4 or 5? Can someone explain why the answer is 2/5 please, thanks.
0
votes
2answers
32 views

rolling dice 6 times, outcomes showing of 2 sixes

If 6 dices are rolled, in how many ways will exactly 2 sixes show up? I was thinking that it would be 6*6*5*5*5*5, am I right?
0
votes
2answers
45 views

Probability of selecting one of multiple sets of distinct items

Here is the problem I am having: You have a set of items; let's say colored stones. There are 40 stones. 3 Blue, 3 Red, 3 Green, 3 White, 3 Yellow, 3 Purple, 3 Orange, 1 Black, 18 Grey. Without ...
0
votes
0answers
9 views

Proving a disequality involving hypergeometric distribution

How would you prove symbolically the following property? $$H(m_a+1,p_a+1,m,p) < H(m_a,p_a,m,p)$$ where $H(m_a,p_a,m,p)$ is the probability of drawing $m_a$ white balls in a series of $m$ ...
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
22 views

Combinatorics Drugs Distribution

Someone already asked this question but I wanted to know why the answer isn't $ {50\choose20} + {30 \choose 20 }+ {10 \choose 10 } $ instead it's $ {50\choose20} \cdot {30 \choose 20 } \cdot {10 ...