Questions on using, finding, or otherwise relating to probability distributions, pdfs, cdfs, or the like.
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Computing Conditional Probability (Poisson Random Variables)
The number of red and blue cars that go through a given intersection in an hour is a Poisson-distributed random variable with $\lambda$ = 10. What is the probability, conditionally, that at most ...
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Inferring properties of unknown distribution functions
Let $F(\theta)$ be an arbitrary, strictly increasing and twice differentiable CDF that is defined on the interval $[0, \overline{\theta}]$, where $\overline{\theta}$ may be infinite. Moreover, let ...
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24 views
Method to show independence of discrete random variables
I thought I would be able to do these problems, all I can find are proofs that if random variables are independent that the product of distributions is the joint distribution of the two. I cannot ...
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1answer
31 views
calculating cumulative distribution function $F_X(x)$ of the problem
Suppose we have a street intersection. It consists of a center point and 4 one-mile-long streets from the center. Street 1 points up, street 2 points down, street 3 points to the right and street 4 ...
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27 views
Testting independence probability given a joint density function
Two continuous random variable A and B have a joint density function
f(A,B)(u,v)=m⋅min{a,1-a,b,1−b}for 0≤a≤1 and 0≤b≤1
m is a positive number. For example, f(A,B)(0.3,0.4)=m⋅min{0.3,0.4,0.7,0.6}=0.3m.
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1answer
16 views
Conditional Probability with marginal densities
X and Y have the joint denstiy:
$f(x,y) = 2x+2y-4xy$ for $0< X< 1$ and $0< Y< 1$
and 0 otherwise.
.
(a) Find The marginal densities of X and Y
I got both marginal densities equal to 1 ...
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1answer
19 views
Conditional Probability Proof
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)|X = x] = E [h(x,Y )]
Explain why this is usually not true if X and ...
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1answer
29 views
Conditional Expectations: Calculating E(Y|X=x) and E(X|Y=y)
X1 and X2 are independent and uniformly distributed on {1,2,...,n}. Let X be the minimum and Y the maximum of X1 and X2. Calculate:
(a) E(Y|X=x)
(b) E(X|Y=y)
I tried making distribution tables for ...
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1answer
17 views
Conditional Probability Given N=n
suppose that $N$ is a Poisson$(μ)$ random variable. Given $N=n$, random variables $X_1,X_2,X_3,\cdots,X_n$ are independent with uniform∼$(0,1)$ distribution. So there are a random number of $X$'s.
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1answer
36 views
What is the difference between a probability distribution on events and random variables?
For the purpose of simplicity, assume everything below is only in the discrete domain.
A $\text{probability space}$ is usually defined as a triple $(\Omega , 2^\Omega , P)$ where
$\Omega := ...
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1answer
40 views
find the cummulative distribution function FX(x) given an image above
Suppose we have a street intersection. It consists of a center point and 4 one-mile-long streets from the center. Street 1 points up, street 2 points down, street 3 points to the right and street 4 ...
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2answers
38 views
Distribution of sum of independent random variables
Let $X$ and $Y$ be independent random variables taking values in $[0,1]$ where $X$ is uniform. Question is, what distribution on $Y$ will yield a uniform distribution on $[0,2]$ for the sum $Z=X+Y$?
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0answers
32 views
Coupling of Gaussian Random variables.
Suppose I have two mean zero multivariate Gaussian random variables $X$ and $Y$ on $\mathbb R^d$, with covariance matrices $A$ and $B$. (Assumed to have full rank).
I have many choices of joint ...
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22 views
Number of ways to distribute balls in boxes if each ball is able to be in several boxes simultaneously.
Consider $n$ balls and $k$ boxes and assume that each ball may be in one or more boxes. If there're no any interactions among balls or boxes, then the question is, how many possible distributions if
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3answers
38 views
if we flip the coin $100$ times, what is$ P(X\leq 10)$?
we have a coin of diameter $d$ and a table of infinite grid of identical squares, each square has side $s$. suppose that $2d = s$. let $X$ denote the total number of times that the coin ends up within ...
