Tagged Questions
0
votes
2answers
65 views
Finding the probability of given model
I'm trying to model a system given as a project, any help or advice is useful for now.
Here our assumptions for a part of it:
If I study for the finals and do assignments, I have $80\%$ chance to ...
2
votes
0answers
43 views
A question regarding the central limit theorem
I would appreciate if you could please take a look at the following attempt. I am preparing for an upcoming exam, and this is taken from a past exam paper. I would like to know if it is correct. Thank ...
-1
votes
0answers
51 views
satellite radios has a 3% defective rate. A random sample of 1000 radios is drawn. What is probability the defective rate is greater than 5%?
The assembly line that produces satellite radios has historically resulted in a 3% defective rate. A random sample of 1000 radios is drawn. What is the probability that the defective rate is ...
1
vote
0answers
49 views
Mean and variance of call center data
I have a fairly involved homework question, I was wondering if I could get some help.
There are two types of phone calls arriving at a switch, long-duration and short-duration. Each day the number ...
1
vote
1answer
56 views
Moment generating functions question
Suppose that $X_1, X_2, ..., X_n$ are independent, where each $X_i$ has probability (mass) function $p_i(x_i)$ given as $p_i(x_i) = \frac{e^{-\lambda} \lambda_i^{x_i}}{x_i!}$ (only the parameter ...
4
votes
3answers
198 views
Probability the sum of numbered balls drawn from a box is odd
A box contains 100 balls, numbered from 1 to 100. If 3 balls are selected at random and with replacement from the box, what is the probability that the sum of the 3 numbers on the balls selected from ...
2
votes
2answers
88 views
Using the Bayes Theorem?
A certain town has two taxi companies, the Green Taxi Co (cars coloured green) and the Blue
Taxi Co (cars coloured blue). 10% of taxis are the Green and 90% are the Blue. There was an
accident ...
0
votes
0answers
17 views
Tolerance as the probability of success
Often you try to find the number of samples needed (at least a lower bound) to meet a certain level of tolerance $ε$ that is usually given as some sort of absolute value. Generally done like so:
• $n ...
0
votes
0answers
47 views
the expected value of your gain
You flip a coin and if it is a head I pay you 1 pound but if it is a tail you pay me 2 pounds. You have 50 pounds and you stop when you spend all of your money or you flipped coin 100 times. What is ...
0
votes
0answers
60 views
Joint Cumulative Distribution Functions (with Marginal Properties)
I have encountered a joint cumulative distribution function with marginal properties. Although I have the answer, mine doesn't really match it and I don't seem to understand why.
IMG: ...
0
votes
1answer
41 views
Interpreting probability conditions from question
I've encountered this question:
And got the answer here:
However, what I don't quite understand is how are the two conditions derived from the question in the first place.
1
vote
1answer
76 views
How to calculate minimum of multiple exponential distributions?
$X_1$, $X_2$, $X_3$ are independent random variables, each with an exponential distribution, but with means of $2.0, 5.0, 10.0$ respectively. Let $Y$= the smallest or minimum value of these three ...
0
votes
1answer
33 views
Expression of probability
Given the following question...
I'm still unclear why it's
$$P(T|L)$$
and not
$$P(L|T)$$
Appreciate any advice please.
0
votes
1answer
62 views
Birthday problem, but matching couples instead of individuals
Suppose n couples are invited to a party. What is the probability that there are at least
two husband–wife pairs such that the husbands have the same birthdays and so do their
wives?
1
vote
0answers
33 views
Study- Probabilities problem
Can some of you tell me why the following holds true?:
$ P(A \& B^C )= P(A)-P(A\&B)$ in which: $ B^C$ is $B$ complement.
In which: $A$ and $B$ are independent.
thanks..
0
votes
0answers
51 views
How to compute probabilities of normally distributed variables?
Let $X_1, X_2, \ldots, X_{16}$ be independent with $N(3,4)$ distributions and $\bar{X}$ denote the sample mean. Find:
$P(-8 < 2 \bar{X} < -4)$.
A number $K$ such that $P(-K < 2 \bar{X} ...
-1
votes
1answer
70 views
calculate joint Probability density function limit distribution of statistics $T_n=(nU_{(1)},nU_{(2)}).$
Suppose $U_{(1)} , \dots , U_{(n)}$ is order statistics a random sample from $U(0,1)$.how can find joint Probability density function limit distribution of statistics $T_n=(nU_{(1)},nU_{(2)}).$
-4
votes
1answer
110 views
Maximum Likelihood Estimator (MLE)
Salmon sometimes carry a parasite anisakis simplex which they pick up when feeding on krill at sea. The number of parasites on each fish might be assumed a random variable X having a probability ...
0
votes
2answers
70 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 ...
1
vote
1answer
97 views
Why are the Borel subsets on $\mathbb R$ a $\sigma$-algebra?
I am a newbie in mathematical statistics and haven't learnt any group theory before. My lecture notes are too brief. How can the Borel subsets on $\mathbb R$ satisfy A.2 and A.3 of a $\sigma$-algebra ...
0
votes
1answer
71 views
Probability of 2 uniformly randomly generated, n-digit numbers (n>=4) having the same last 4 digits?
I apologize if question is too simple!
For example, is the probability of generating 2, 8-digit numbers that have the last 4 digits match the same as the probability of the last 4 matching with a 12 ...
0
votes
2answers
193 views
How does variance change as sample size increases
Situation:
n possibilities each have their own probability of happening, and their own payout when they do.
So expected payout $E_n$ is $\sum\limits_{i=1}^n \text{probability}_i*\text{payout}_i$
...
0
votes
2answers
122 views
Bayesian inference with Gaussian distributions
This is Problem 4(c), Chapter 2 from Thrun's Probabilistic Robotics . Note that this is self-study and not homework.
Suppose I know my position $x$ to be a normal distribution with density ...
0
votes
0answers
41 views
May I get HMM calculations Checked?
I was trying to understand Hidden Markov Model(HMM). I was working out some examples.
The first work out was on initial probability, transition probability and emission probability.
I was trying to ...
0
votes
0answers
49 views
Are my HMM calculations going fine? [closed]
I was trying to understand the hidden Markov model (HMM) and to do some calculations, and I got some doubts. I attach my study in this Google Drive File.
Can you check if my calculations are fine?
I ...
2
votes
1answer
45 views
Probability proofs using ordered samples
Given an ordered i.i.d sample $X_{(1)}, \dots, X_{(n)}$ from a continuous distribution $F(x)$. How can it be shown that:
(1) $\text{Pr}(X_{(k)} \leq x) = \text{P}r(N(x) \geq k)$
where $N(x)$ is the ...
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), ...
1
vote
0answers
80 views
Conditional probability questions (homework)
I copied the exact question. Can anyone check my answer? I am so confused between the choices, all of them seems to be workable.
An company divides their customers according to how long they take ...
0
votes
0answers
49 views
Normal Distribution [duplicate]
Using the normal distribution. Let $X\sim \mathcal{N}(1, 2)$ and $Y\sim \mathcal{N}(2, 3)$ where $\mathcal{N}(μ, \sigma^2$)
denotes the normal distribution with mean $\mu$ and variance $\sigma^2$. X ...
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
1answer
327 views
probability of one random variable being greater than another
Using the normal distribution. Let $X \sim N(1, 2)$ and $Y \sim N(2, 3)$ where $N(\mu, \sigma^2)$ denotes the normal distribution with mean $\mu$ and variance $\sigma^2$. $X$ and $Y$ are independent.
...
2
votes
2answers
163 views
Probability of picking a biased coin
Suppose you have a bag of 100 coins of which 1 is biased with both sides as Heads. You pick a coin from the bag and toss it three times. The result of all three tosses is Heads. What is the ...
2
votes
2answers
70 views
0
votes
0answers
103 views
How to derive the conditional posterior density in hierarchical bayesian models?
I was reading on Gelman's Bayesian Data Analysis - Chapter 5 - Hierarchical model
Suppose:
data : $y_j$ s
parameter: $\theta$
hyperparameter: $\phi$
On page 126, he mentions the analytical ...
1
vote
0answers
100 views
How to set up a posterior predictive test quantities (Bayesian context) to check for independent Poisson distributions?
Suppose we are given data $y_j \sim \text{Poi}(\lambda)$ and assume $y_j$ are iid.
We can assume the prior distribution for $\theta$ follows $\text{Gamma}(\alpha, \beta)$,
The posterior ...
2
votes
1answer
89 views
Realizations of random variable
Can some of you help me with following exercise?
Provide a procedure to generate realizations of a random variable with
CDF (cumulative distribution function) $Fx(x)$ given by:
...
0
votes
1answer
73 views
Average waiting time
who can help me to resolution of this statistic exercise? below the track: Caio go in a bank,the number of customers ahead him are described by a Poisson random variable of parameter a>0. Calculate ...
0
votes
2answers
132 views
How to compute the PDF of a sum of a discrete and a continuous random variable? [closed]
I have a problem with this exercise in probability and statistics:
Calculate the probability density function (PDF) of
$$Z=X+Y$$
where $Y$ is discrete random variable which is equal to $-1$ and $1$ ...
3
votes
1answer
107 views
Convergence in distribution and CDF
Suppose $X_n$ converges in distribution to $X$ , $x_n \rightarrow x$, also the cumulative distribution function for $X$ is continuous at $x$. Show that $ P(X_n \leq x_n) \rightarrow P(X \leq x)$.
...
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 ...
0
votes
2answers
249 views
Wigan scores after 30 minutes. Calculate home, away and draw in percentage terms with poisson regression
I have the following exercise:
Wigan v city 90 mins match:
Wigan scores after 30 minutes.
Calculate home, away and draw in percentage terms with poisson
regression, assuming pre-match odds ...
2
votes
3answers
115 views
Find the limiting distribution of $W_n$
Having a little trouble with this one:
Suppose $X_1, X_2, \ldots $ are iid standard normal random variables. Let $W_n = \sqrt{n} \frac{X_1 + \cdots + X_n}{X_1^2 + \cdots + X_n^2}$. Find the limiting ...
0
votes
1answer
94 views
How to find the joint density of 3 normal variables?
Suppose $U, W, V, S$ are four independent normal random variables with mean $0$ and variance $1$. Let $X=W+U$, $Y=2W+S$, $Z=3W+V$. What is $f(X, Y, Z)$?
Thanks!
2
votes
0answers
174 views
How to find principal components from variance-covariance matrix?
If I have the following var-cov matrix:
$\Sigma_{A,B,C} = \left(\begin{array}{ccc}
1 & 2 & 3 \\
2 & 4 & 6 \\
3 & 6 & 9 \\
\end{array}\right)$
(1) How can I find a constant a, ...
0
votes
0answers
44 views
About Galton watson process
My question is about a homework question that I found interesting. It gives another proof (without using martingales) for that the critical Galton Watson tree dies out eventually. But it has given a ...
6
votes
1answer
153 views
Probability that at least one person at a party will accidentally choose their own gift
Thirty people are invited to a holiday party, where a gift exchange will take place. Each person brings a gift to put into the pot, and at the end of the night each person selects—at ...
2
votes
0answers
55 views
Conditional distribution of quadratic forms
Given that $Y$ follows multivariate normal distribution ,i.e, $N_n (0, \sigma^2 I_n)$, we want to find the distribution of $Y'Y$ given that $a'Y=0$ where $a$ is a non zero constant vector.
I know ...
1
vote
2answers
171 views
Non-fair die - College Probability
How many times must you roll a non-fair die to be at least 84% sure that the sample probability will be within 3% from the actual probability.
Since the die is not-fair, we do not know p. My question ...
1
vote
0answers
30 views
Sampling distributions help with questions [duplicate]
Possible Duplicate:
Probability of mean of random sample being in a certain range
When a pizza restaurant’s delivery process is operating effectively, pizzas are delivered in an average of ...
