Tagged Questions
0
votes
0answers
51 views
Distribution of independent binomial variables conditional upon the sum
Suppose that we have independent binomial variates with differing sizes and probabilities $X_i \sim Binomial(n_i,p_i)$, and $Z = \sum_iX_i$ is the sum. I understand that $Z$ is distributed ...
0
votes
1answer
31 views
Finding the bionomial probability?
Ok so i have been taught this formula regarding binomial probability
Repeat an even n times
...
0
votes
2answers
69 views
Normal approximation to binomial
What do I do when the normal approximation is not valid?
Here's the question I'm trying to answer:
A student guesses all 15 answers on a multiple-choice test. There are 5 choices for each of the ...
2
votes
1answer
40 views
Binomial probability function
What is the probability of rolling exactly two sixes in 6 rolls of a die?
Solution by the Binomial Probability formula is
$$\binom{6}{2} \left(\frac{1}{6}\right)^2 \left(\frac{5}{6}\right)^4 = ...
1
vote
1answer
29 views
How many measurements (10 million molecules each time) are needed to analyze 15 million unique molecues in a 20 million pool?
This is my homework: There are 20 million DNA molecules in a library for high throughput DNA sequencing, each sequencing run can generate 10 million reads (i.e., analyze 10 millions of DNA molecules), ...
0
votes
1answer
235 views
Finding the z score and p-value of a binomial distribution
Emily is a big fan of lady gaga, and 20% of the songs on her ipod are lady gaga songs. Suppose Emily has her ipod on shuffle and repeat mode, which can be assumed to mean that each song to be played ...
0
votes
2answers
109 views
Why doesn't this represent a normal approximation to the binomial?
Suppose the registrar's office at a college reports 58% of the students live on campus. An intern working in the administration building is unaware of this 58% parameter value. He designs a study in ...
2
votes
2answers
108 views
Binomial distribution where probability of success is dependent on another binomial distribution
How does one model the Binomial distribution where the probability of success is the result of another Binomial distribution.
For example, say I make 10 coin tosses many times and record the number ...
3
votes
2answers
51 views
Which test should I use?
I have a set of probabilities that an event will occur (yes/no). E.g. [0.87, 0.56, 0.97], and I need to know "What is that probability that at least X of these events occurs?". I've been looking into ...
0
votes
2answers
83 views
Calculate a tennis players chance to win a 5set match knowing he has 50% chance of winning 1SET?
Is the following correct? My friend tells me i need to (add up the binomial probabilities of 2 wins in 2 sets, 2 wins in 3 sets and 2 wins in 4 sets THEN multiply the sum obtained by p)
P(3) = 5C3 x ...
-1
votes
2answers
211 views
Best book to learn probability - poisson, binomial, regression, etc
What is the Best book to learn probability - poisson, binomial, regression, etc.
I am working as an odds adjuster at a bookmaker and need to advance my skills to an odds compiler level.
1
vote
2answers
198 views
Distribution of number of Bernoulli trials given number of successes
Suppose you have a series of n trials, where the probability of success
in each trial is p. The distribution of the number of successful trials
follows a Binomial distribution with parameters (n, ...
2
votes
1answer
98 views
What is the probability that a sample value from a Binomial distributions is smaller than a sample value from another?
Let $X \sim \mathrm{Binomial} (n, p_1)$ and let $Y \sim \mathrm{Binomial} (n, p_2)$ with $n, p_1$ and $p_2$ known and $p_1 < p_2$.
What is the probability that a sample value $x$ drawn from $X$ is ...
-1
votes
1answer
90 views
Find the probability distribution of X? [closed]
Suppose Nokia store places 20 of its cell phones on a clearance sale, unknown to anyone 5 of these cell phones are defective. A customer selects 3 cell phones at random for inspection. Let X be the ...
0
votes
0answers
40 views
binomial approximation - precision errors
For an estimation problem, i have to compute binomial probabilities given high n,x and low p.
Specifically, I compose a matrix A, whose entries are 0 if i >j , and dbinom(x=j, size=i, p) if i<= ...
3
votes
1answer
68 views
Generating non-zero binomial probabilities (n,k ) with small p and large n - k
I am trying to generate binomial probabilities (in R) as follows:
${N \choose{k}} p^{k} (1-p)^{(n-k)}$
My problem is given $p \approx 0.03$, and $N =400$, $k>270$, I get the probability equal to ...
-1
votes
3answers
473 views
The meaning of P(X=0) in a binomial distribution
recently I was resolving an elementary problem about binomial distribution, this problem requests to determinate $P(X<=2)$, where $X$ is nonconforming products, sample is 50 units, and the fraction ...
1
vote
1answer
65 views
Intuition behind result for binomial
We are given the following equality:
$B(k;n,p)=B(k;n+1,p) + pb(k;n,p)$
where $B$ is the binomial cdf, $b$ is the binomial pdf, $n$ is the number of trials and $p$ is the probability of success.
How ...
0
votes
1answer
125 views
Probability of winning a drawing/lottery
I can't seem to get my head around this: A random drawing will be held for which there are 900 tickets sold, for which there will be one winning ticket drawn. If you purchased 25 tickets, what is the ...
0
votes
2answers
150 views
Probability that the probability for a binomial distribution is below a certain value
This is a slightly odd problem I ran across recently. Assuming a population of size $N$ following a binomial distribution with unknown $p$, how many different samples must be taken from the population ...
1
vote
0answers
73 views
Question related to binomial distribution
Let $X \sim Binomial (n, p)$ with both $n$ and $p$ known.
Suppose for some non-increasing function $G:[0,1] \rightarrow [0,1]$,
and some fixed $c_0 \in [0,1]$,
we have that
\begin{align} ...
3
votes
1answer
117 views
Cumulative distribution of Binomial Random variable
How to prove this:
Proposition. If $F_n$ is the distribution function of a $\textrm{Bin}(n,p)$ random variable, then, for every real fixed $t$, the sequence $\{F_n(t)\}_{n=1}^\infty$ is ...
0
votes
0answers
22 views
how do I find out the probability of having 3 left handed people in a random group of 5 people. Assuming .90 probability of right handedness [duplicate]
Possible Duplicate:
Probability of getting between
I have tried to solve this in several ways. I treated it as a Bernoulli trial and multiplied .9 (the probability that one person is right ...
0
votes
3answers
157 views
How to compute the number of games that must be played for the better team to win 70% of the time?
I've been stuck on this sample statistics problem for a couple days now:
Assume that two baseball teams have win records of $58\%$ and $54\%$. Demonstrate how to compute or estimate the number of ...
0
votes
1answer
80 views
What is the distribution for modeling the number of successes in a specific order in N trials?
The Binomial distribution models the number of successes in N trials, but the successes can be in any order. What's the distribution for when the successes have to be in a specific order? Do you just ...
3
votes
2answers
260 views
Probability over multiple blocks of events
I'm trying to find the probability of getting 8 trials in a row correct in a block of 25 trials, you have 8 total blocks (of 25 trials) to get 8 trials correct in a row. The probability of getting any ...
1
vote
1answer
69 views
Error count limit for known residual failure rate and desired false-positive rate?
We perform a known fixed number $K$ of independent experiments, each of which has known/assumed residual odds $p$ to fail. We count the number $N$ of failures. How can I choose $M$ so that $N>M$ ...
1
vote
2answers
129 views
probability of the next number of events occurring when the true probability is known [duplicate]
Possible Duplicate:
Probability of getting between
What is the probability that at least 24 of the next 50 people like to swim when the true probability of people liking to swim is 35%?
I ...
2
votes
1answer
91 views
How to determine larger probability of drawing one element from a set when set size and number of draws with replacement vary?
Which is the better scenario in terms of probability with the following:
Scenario 1
I have a hat with 5 tickets in it (I have one).
There is one single draw.
I have a 20% chance that my ticket is ...
8
votes
2answers
1k views
Probability distribution for different probabilities
If I wanted to get the probability of 9 successes in 16 trials with each trial having a probability of 0.6 I could use a binomial distribution. What could I use if each of the 16 trials has a ...
2
votes
1answer
72 views
Estimating variability of unseen factor
I'm looking at binomial data where I believe that the probability of the outcome is the product of two independent factors. If you think of it as a two step decision,
At the first step, there is a ...
2
votes
3answers
254 views
Binomial Probability Question
Given two basketball players.
John made 38/50 free throws.
Mike made 80/100 free throws.
What is probability that Mike is better at free throws than John?
2
votes
1answer
375 views
Normal distribution and weight of babies problem
X is the weight of a baby when born (in gram). If the distribution of X is N(3315, 575) and Y is the number of babies with weight lower than 2719 in a random sample of 25, then P[Y≤4] is about...?
...
3
votes
1answer
130 views
Probability of getting between
...2 to 5 questions answered correctly, out of 20 of them? Each question has 5 choices. Probability of getting one right is 1/5. Probability of getting exactly 1 right is ${20 \choose 1} p^1 q^{19}$, ...
3
votes
3answers
928 views
Odds at least 1 person is born in January?
There are 100 people in a room.
What are the odds at least 1 person is born in January?
What is the best way to calculate this?
I used Binomial Distribution.
$E(x) = np = 100 \frac{1}{12} = 8.3$
...
5
votes
1answer
296 views
How can you approximate the number of trials to success given a particular Pr(Success)?
I'm uncertain whether I should be able to intuit the answer to my question from a question that has already been asked but I can't, so I am asking the question anyway. Thus, I am looking for a clear ...
5
votes
3answers
386 views
Non-trivial bound for $E[\exp(Z^2)]$ when $Z \sim {\rm Bin}(n, n^{-\beta})$ with $\beta \in (0,1)$
How to find a non-trivial upper bound on $E[\exp(Z^2)]$ when $Z \sim {\rm Bin}(n, n^{-\beta})$ with $\beta \in (0,1)$? A trivial bound is obtained for substituting $Z$ with $n$.
A background on this ...
