Tagged Questions
1
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0answers
55 views
How does this violate probability theory?
Given: $X = Y^2 + Z^2$ (hence $E[X] = E[Y^2] + E[Z^2]$)
$p(X = 1) = .52$, $p(X = 4) = .24$, $p(X = 16) = .24$
$p(Y = -1) = .5$, $p(Y = 3) = .5$
Question: Despite not being handed any information ...
1
vote
1answer
44 views
distribution function of time T
an ambulance station is located 30 miles from one end of a 100-mile road. the station services accidents along the entire road. suppose that an accident occurs. suppose that Suppose accidents occur ...
0
votes
0answers
27 views
distribution function and density function
A lion is standing $30$ meters from one end of a $100$-meter road. The lion will attack any zebra that appears on the road. Suppose that a zebra appears on the road, and suppose that the position at ...
0
votes
0answers
29 views
Number Plate Problem
I'm having trouble with a question that seems to perplex:
A number plate contains three letters followed by three numbers. A number plate is selected at random.
Calculate the probability that the ...
1
vote
1answer
18 views
Marble Possibility P(At least one yellow)
There are $2$ black and $3$ yellow marbles in a bag. $2$ marbles are drawn randomly without replacement. What is the possibility that at least $1$ yellow marble is selected.
-3
votes
1answer
47 views
Probability of purple party voters in a samaple prediction of two cities A and B
City A has 1,000,000 people; City B has 4,000,000 people. Suppose the goal is to try to predict the percent of Purple Party voters in a sample. Other things being equal, a simple random sample of 1% ...
0
votes
1answer
66 views
probability density functions
Suppose $Y$ is a random variable pdf $f(y)=ky , y=3/n,6/n,9/n...,3n/n$
Find the value of the constant $k$ and write down $Y$'s cdf.
Find simple general expressions for $EY, \text{Var} \,Y, P(Y=3/2)$ ...
0
votes
2answers
26 views
prove by induction that $P\left(\bigcup\limits_{i=1}^{n} E_i\right) = 1-\prod\limits_{i=1}^{n}(1-P(E_i))$, $E_1,E_2,\ldots , E_i$ independent
Suppose $E_1,E_2,\ldots , E_i$ are independent events. prove by induction that $$P\left(\bigcup\limits_{i=1}^{n} E_i\right) = 1-\prod\limits_{i=1}^{n}(1-P(E_i))$$
The first step is easy. For $n=1$ we ...
0
votes
1answer
27 views
probability that a random line segment parallel to the hypot. of a triangle with legs 3 and 4 will inclose an area of at least half
Sorry for the unclear title. It was difficult to explain the problem in a concise way in 150 characters.
A right triangle has the legs 3 and 4 units, respectively. Find the probability that
a line ...
2
votes
1answer
38 views
Cramer-Rao Lower Bound
Assume that $X_1,X_2,\ldots,X_N\sim N(\mu,2^2)$ and $Y_1,Y_2,\ldots,Y_M\sim N(0,\sigma^2)$.
a)Find the Cramer-Rao Lower Bound (CRLB) for the variance of the unbiased estimators of $\mu$.
b)Find the ...
1
vote
1answer
25 views
Calculate gas-station probabilities
I would like to calculate probabilities for the next exercise:
Knowing the average amount of cars that drive per minute into a gas-station is 3.
** How can I calculate the probability of arriving at ...
0
votes
0answers
16 views
stability number of random graphs with constant $p$ and $p=p(n)$
If we know that
$$ \lim_{n \rightarrow \infty} p\left(\alpha(G) \geq \frac{n}{2l}\right)=0$$
where $l$ is a positive integer, $p=p(n)$ is a function of $n$ such that $p \geq (6l\ln(n))/n$ for $n$ ...
0
votes
0answers
32 views
Degree distribution of a random graph
I stuck on the following problem
If a given vertex in a random graph has degree $k$ with probability
$${{{n-1}}\choose{k}}p^k(1-p)^{n-1-k}$$
What can we conclude about degree distribution of $G$. ...
1
vote
1answer
26 views
Difference of Poisson r.v's. Is there a simpler way?
Here's a problem I'm having trouble with (section on Poisson r.v.'s):
Suppose that when a baby is born, the probability it's a boy is $0,52$ and the probability that it's a girl is $0,48$. On some ...
0
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0answers
23 views
Difference of normal r.v's. Please check my answer.
The length of a box is normally distributed with: $X \sim N(50;1.2)$
The length of a drill is normally distributed with: $W \sim N(49;1.2)$
Find the probability that a randomly selected drill will ...
1
vote
1answer
18 views
Poisson distribution question, tips needed!
A car dealership opens every day with a fresh stock of $A$ cars. Let $N$ be the r.v. corresponding to the number of purchases per day. Suppose $N$ is distributed according to the Poisson distribution ...
1
vote
2answers
30 views
Checking independence of random variables.
I'm revisiting the coupon collector's problem and I'm not sure how to prove that my variables are independent. Here's what I have:
Let $X$ denote the number of tries required to collect all the ...
2
votes
1answer
23 views
Basic independent probability question
This question is a homework question.
The question states:
An airline can seat 100 people. Historically, the airline has noticed that each customer shows up independently and with probability ...
-2
votes
1answer
33 views
Why is this expectation calculation wrong?
Let
$E(X|A)=2+E(X)$
$E(X|B)=3+E(X)$
$E(X)=0.5E(X|A)+0.3E(X|B)$
Now to find $E(X^2)$ I did
$E(X^2|A)=4+E(X^2)$
$E(X^2|B)=9+E(X^2)$
$E(X^2)=0.5E(X^2|A)+0.3E(X^2|B)$
What did I do wrong here?
...
0
votes
1answer
55 views
Wrong Reasoning about the problem of breaking a stick in $2$ points and build a triangle with the $3$ parts.
For homework I was asked to solve this classical problem "If you break a stick at two points chosen uniformly, the probability the three resulting sticks form a triangle is 1/4" and ok, it must result ...
1
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0answers
39 views
Probability of Roulette on a Split and on Red comparison
In roulette, the bet on a “split” pays 17 to 1 and there are 2 chances in 38 to win. The bet on “red” pays 1 to 1 and there are 18 chances in 38 to win. Compare the following two strategies:
A: bet ...
0
votes
2answers
28 views
expected number of edges in a random graph
If we have a random graph $G \in g(n,\frac{1}{2})$ how do we show that the expected number of edges is $\frac{1}{2} {{n}\choose{2}}$
Thanks in advance
0
votes
1answer
27 views
complement of a random graph
If we have a random graph $G_p \in g(n,p)$ how would we show that the complement $\bar{G}_p$ is eqaul to $G_q \in g(n,q)$ where $q=1-p$?
I'm finding it hard to start this sort of proof so any help ...
0
votes
2answers
30 views
marginal and conditional distributions
A project has two phases. Let $X$ be the time (in months) required to do phase 1 and Y be the total time (in months) it takes to complete both phases. Suppose that the joint density of $X$ and $Y$ is ...
1
vote
0answers
61 views
Spatial distribution of bees
* Please please help! I still get stuck.
We have a forest for bees, consisting of $4$ non-overlapping regions. $80\%$ of the bees seek honey in the forest while $20\%$ of the bees do so outside the ...
1
vote
0answers
32 views
Inequality with $\|\cdot\|_p$ norm
Let $x_1, \ldots, x_{2m}$ be $\{0,1\}$ Bernoulli random variables, i.e. variables which takes values $0$ and $1$ with equal probability. Let $S_m$ be group of all permutations $\pi$ on $\{1, \ldots, ...
1
vote
2answers
53 views
A probability question: a building and an elevator.
Suppose that 7 people waiting for an elevator in a building with 14 flours.
Q: What is the probability that every person get out in different flour?
My attempt:
There is $14 \cdot 13 \cdot 12 \cdot ...
2
votes
2answers
34 views
Finding probability's distribution and calculation
I am trying to understand what is the implied distribution of the following problem:
A student asks for help from the professor 2 times per test on average.
the student took 5 different test
a) what ...
1
vote
1answer
33 views
Finding a probability distribution given the moment generating function
The $n$-th moment ($n \geq 1$) of a random variable $X$ is given by: $m_n = \frac{2^n}{n+1}$. Find the probability distribution of $X$.
Here's my attempt at a solution: I expand the moment generating ...
2
votes
1answer
145 views
Another hat problem
A finite number of prisoners, after being given their hats (black or white), are able to see one another but themselves, and then they are ordered to jot down their guess on the color of their own ...
-5
votes
1answer
472 views
Help for solution! [closed]
The durations of phone calls taken by the receptionist at an office are like draws made at random with replacement from a list that has an average of 8.5 minutes (that's 8 minutes and 30 seconds) and ...
1
vote
1answer
18 views
Special probability distributions
In a box there are $10$ balls numbered $1,2,...,10$. We're taking out balls one by one until we take out the ball numbered $5$. Let $X$ be the number of balls take outs, find the probability ...
0
votes
1answer
44 views
Find the maximum likelihood estimator for $\theta$ when $f(x)=2\theta^{-2}x, 0\leq x \leq \theta$
Find the maximum likelihood estimator for $\theta$ when $f(x)=2\theta^{-2}x, 0\leq x \leq \theta$.
This should be a really easy question but I somehow cannot seem to get the right answer. My ...
1
vote
1answer
39 views
Bayes theorem for calculation with personal probabilities
I'm completely stuck on some homework I have and can't figure it out.
The task is to calculate the probability of a bus being late conditional on the weather being snowy and bus driver being ...
0
votes
0answers
22 views
Possion process with 2 variable
I have a burning question. Please help
Both A and B suffer kidney disease and require kidney transplant. If A does not received a new kidney, he will die after an exponential time with rate u(a). ...
0
votes
2answers
35 views
to calculate standard deviation using mean and sample size
Given the mean as 1336 and sample size as 24, how to calculate standard deviation when the deviation scores and sample figures are unknown.
2
votes
3answers
81 views
Check my answer: A slight modification to the 'hat-check' problem.
Suppose $n$ (hat wearing) people attended a meeting. Afterwards, everyone took a hat at random. On the way home, there is a probability $p$ that a person loses their hat (independent of whether other ...
0
votes
0answers
34 views
Conditional expectation proof [duplicate]
Suppose that $X$ and $Y$ are independent discrete random variables. Let $h(x,y)$ be a bounded two-variable function.
Show that: $E[h(X,Y)\mid X = x] = E[h(x,Y )].$
Explain why this is not usually ...
1
vote
1answer
23 views
Probability homework help
I need help with a simple homework exercise.
How to find $\Pr(A)$ if:
$$\Pr(A|B) = 0.2 $$
$$\Pr(B) = 0.8 $$
$$\Pr(A|B^c) = 0.3$$
I found $\Pr(A\cap B)$ and $\Pr(A\cap B^c)$ but I don't know what to ...
-1
votes
0answers
20 views
Probability that difference sample mean from population mean is 1.96 sd [closed]
Probability that difference sample mean from population mean is 1.96 sd
a)68%
b)95%
c)47/5%
d)99%
2
votes
3answers
60 views
Homework Question. Joint Probability Distribution.
Here is the question.
The joint PDF of X and Y is given by $f_{XY}(x,y) = {\frac 14} e^{-|x|-|y|}$. Find $P(X \le 1 ,and, Y \le 0)$
Solving the problem I first found the marginal probabilities of X ...
0
votes
0answers
30 views
Homework Help. Probability Density Functions.
$X$ is $N(10,1)$. Find $f(x|(x-10)^2 < 4)$
This is a homework question. I can only figure out that X is normally distributed with mean 10 and variance 1.
Can you please explain what is meant to ...
-2
votes
1answer
65 views
Finding the normalizing constant and marginal densities given a joint density
Two continuous random variable $U$ and $V$ have a joint density function $$
f_{(U,V)}(u,v) = k\cdot\min\{u,v,1-u,1-v\} \quad\text{for }0 \leq u,v \leq 1.$$
Here $k$ is a positive number. For example, ...
0
votes
3answers
31 views
Cumulative distribution function and expected value
I've got cumulative distribution function given: $F_X(t) = 0 $ for $t<0$, $\frac{1}{3} $ for $t=0$ , $\frac{1}{3} + \frac{t}{90} $ for $ t\in (0,60)$ and $1$ for $t \ge 60$. I am to find expexted ...
6
votes
1answer
120 views
The parking problem riddle
Assume a street of 300 meters, that you can park your car alongside the pavement. Assume that there is a big parking problem in the area. Assume that the pavement is continuous, without interruptions, ...
-4
votes
1answer
27 views
What is the distance for 68% people grades?
In the normal distribution, if mean $=12$ and sd $=2$, what is the distance for $68\%$ people grades?
$10-14$
$10-12$
$8-12$
$2-10$
0
votes
0answers
42 views
Generalized Likelihood Ratio Test and Hypothesis Testing
Below is a question from a review sheet on an upcoming final that I am really struggling with. Any help is greatly appreciated!
Let $Y_1, Y_2,...,Y_8$ be a random sample from the uniform ...
0
votes
2answers
23 views
Difficulty in understanding probability of a continuous random variable
My probability textbook (Introduction to Probability Models 9th ed. by Sheldon M. Ross) says that, the probability that a continuously distributed random variable $X$, with probability density ...
0
votes
0answers
26 views
Exponential Order Statistics Independence
Are the order statistics from the $n$-sample with $X_i\sim \text{Exp}(\lambda)$ (taking, without loss of generality, $\lambda=1$) $\Delta_{(k)}X=X_{(k)}-X_{(k-1)}$ independent?
Can show that for an ...
0
votes
1answer
39 views
Check if discrete random variables are independent
I came across this probability question while checking the homework of one of the probability courses at my uni. It's easy but still interesting for very beginner in probability.
Suppose we have two ...
