0
votes
1answer
63 views

Combination Problem with Sofa [on hold]

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
28 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
33 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
73 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
40 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
24 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
31 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
38 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
24 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
37 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
79 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
40 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
65 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
23 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
307 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
93 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
41 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
57 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
24 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 ...
0
votes
1answer
58 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
37 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
31 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
54 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
42 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
19 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 ...
0
votes
1answer
24 views

Probability Discrete Math Bag

A bag contains 15 different objects, 5 red object, 5 blue objects, and 5 white objects. If 3 objects are chosen at random a) What is the probability that 3 objects of the same color are chosen? b) ...
0
votes
1answer
24 views

Probability Discrete Math

{1,2,3,4,5,6,7,8,9} What is the probability that the sum of any of these three numbers is odd? I know that I should use $ n \choose k $ somehow and I know that my professor used this as his equation: ...
0
votes
2answers
185 views

Discrete math: probability of picking certain hands with a preset condition

In 5-card draw poker, a player receives an initial hand of 5 cards, and is then allowed to replace up to three of her cards with the remaining cards in the deck. (b) Suppose that, among the initial 5 ...
0
votes
1answer
43 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, ...
1
vote
1answer
48 views

Expected number of rolls when repeatedly rolling an $n$-sided die

Suppose I roll an $n$-sided die once. Now you repeatedly roll the die until you roll a number at least as large as I rolled. What is the expected number of rolls you have to make? I know the answer ...
1
vote
1answer
44 views

Ping Pong Winning Probability (World Series)

You are playing ping pong with a friend and your chance to win any point is P. This is a world series. Find the probability that you score 4 points before your friend has a score of 4. Evaluate this ...
1
vote
2answers
34 views

How do I calculate variance for sum of dice?

I'll post my work, but I'm not sure how to calculate variance. The question asks for the expected sum of 3 dice rolls and the variance. I think I got the expected sum. Any help would be awesome :) ...
1
vote
1answer
39 views

Probability and Combinations

In a family with 6 children, a. What is the probability of having three children of each sex? b. What is the probability of having four of one sex and two of the other sex? I know in this problem ...
1
vote
2answers
36 views

$K$ events that are $(K-1)$-wise Independent but not Mutually/Fully Independent

I had the following question: Construct a probability space $(\Omega,P)$ and $k$ events, each with probability $\frac12$, that are $(k-1)$-wise, but not fully independent. Make the sample space as ...
0
votes
1answer
62 views

Roll 2 dice adding and rolling one die, probability of being equal

Roll two dice, add the results, call the number x. Roll one die call that number y. What is the probability that x and y are equal? Help please.
0
votes
0answers
23 views

probability in graphs - degree distribution

I am reading this paper on networks which employs probability in analyzing graphs. Suppose that a graph has $n$ vertices. Furthermore, if each vertex has a probability $p_k$ of having $k$ neighbors, ...
0
votes
0answers
17 views

probability of linear expectation with random variables. [duplicate]

I really I have no idea where to start with this question. If anyone could help me out that would be awesome. Let X1,X2,...,Xn be a sequence of mutually independent random variables. For each i with ...
1
vote
1answer
79 views

How do I find the probability of specified events from a permutation of the 26 english letters?

I found a similar problem here, but I don't really understand the explanation to their solution and can't apply it. Question: What is the probability of the following even when we randomly select a ...
0
votes
0answers
16 views

Am I calculating probability correctly?

I am working on some discrete math problems and would like to make sure I'm doing them correctly and what not. Instead of typing it all out in latex, I took a picture of the questions/my work. I hope ...
0
votes
1answer
61 views

Probability of resulting in odd numbered die roll and red suited card?

Roll a die and pick one card from a standard deck. What is the probability that this procedure will result in an odd numbered die roll and a red-suited card? I am guessing 1/4? because odd + black, ...
1
vote
0answers
26 views

Hatcheck Experiment n=2k

I'm sure the famous hatcheck experiment is well known. However I stumbled upon an interesting question. Consider the experiment with $n=2k$ hats, in other words an even number of hats. Find the ...