Actually, I'm just studying singular continuity, absolute continuity.I know the definitions.And have solved few very basic sums. Now, in this problem, I'm not understanding what does this 'with respect to Uniform$(0,3)$' mean! As I know Uniform$(1,5)$(I think in this question 'continuous' uniform has been meant, not sure though) is always continuous. Could anyone help?
2026-02-23 06:03:56.1771826636
Show that Uniform$(1,5)$ is neither singular nor absolutely continuous with respect to Uniform$(0,3)$.
99 Views Asked by Bumbble Comm https://math.techqa.club/user/bumbble-comm/detail At
1
There are 1 best solutions below
Related Questions in PROBABILITY
- How to prove $\lim_{n \rightarrow\infty} e^{-n}\sum_{k=0}^{n}\frac{n^k}{k!} = \frac{1}{2}$?
- Is this a commonly known paradox?
- What's $P(A_1\cap A_2\cap A_3\cap A_4) $?
- Prove or disprove the following inequality
- Another application of the Central Limit Theorem
- Given is $2$ dimensional random variable $(X,Y)$ with table. Determine the correlation between $X$ and $Y$
- A random point $(a,b)$ is uniformly distributed in a unit square $K=[(u,v):0<u<1,0<v<1]$
- proving Kochen-Stone lemma...
- Solution Check. (Probability)
- Interpreting stationary distribution $P_{\infty}(X,V)$ of a random process
Related Questions in MEASURE-THEORY
- On sufficient condition for pre-compactness "in measure"(i.e. in Young measure space)
- Absolutely continuous functions are dense in $L^1$
- I can't undestand why $ \{x \in X : f(x) > g(x) \} = \bigcup_{r \in \mathbb{Q}}{\{x\in X : f(x) > r\}\cap\{x\in X:g(x) < r\}} $
- Trace $\sigma$-algebra of a product $\sigma$-algebra is product $\sigma$-algebra of the trace $\sigma$-algebras
- Meaning of a double integral
- Random variables coincide
- Convergence in measure preserves measurability
- Convergence in distribution of a discretized random variable and generated sigma-algebras
- A sequence of absolutely continuous functions whose derivatives converge to $0$ a.e
- $f\in L_{p_1}\cap L_{p_2}$ implies $f\in L_{p}$ for all $p\in (p_1,p_2)$
Related Questions in PROBABILITY-DISTRIBUTIONS
- Given is $2$ dimensional random variable $(X,Y)$ with table. Determine the correlation between $X$ and $Y$
- Statistics based on empirical distribution
- Given $U,V \sim R(0,1)$. Determine covariance between $X = UV$ and $V$
- Comparing Exponentials of different rates
- Linear transform of jointly distributed exponential random variables, how to identify domain?
- Closed form of integration
- Given $X$ Poisson, and $f_{Y}(y\mid X = x)$, find $\mathbb{E}[X\mid Y]$
- weak limit similiar to central limit theorem
- Probability question: two doors, select the correct door to win money, find expected earning
- Calculating $\text{Pr}(X_1<X_2)$
Related Questions in RANDOM-VARIABLES
- Prove that central limit theorem Is applicable to a new sequence
- Random variables in integrals, how to analyze?
- Convergence in distribution of a discretized random variable and generated sigma-algebras
- Determine the repartition of $Y$
- What is the name of concepts that are used to compare two values?
- Convergence of sequences of RV
- $\lim_{n \rightarrow \infty} P(S_n \leq \frac{3n}{2}+\sqrt3n)$
- PDF of the sum of two random variables integrates to >1
- Another definition for the support of a random variable
- Uniform distribution on the [0,2]
Related Questions in SINGULAR-MEASURES
- Reverse type $1-1$ inequality
- An example of a a convolution of singular distribution and a Gaussian distribution that has a 'simple' pdf
- property of singular measure with respect to Lebesgue measure
- Singular function that is Holder for all $\alpha<1$
- Singular continuous
- Singular bivariate distributions
- Does the Lebesgue measure on the segment $y=x$ represent this distribution?
- Support of a Measure (Singular to Lebesgue)
- Singular Borel measures that are regular and the quotient of it's derivative over itself.
- How we compute expectation of a singular random variable?
Trending Questions
- Induction on the number of equations
- How to convince a math teacher of this simple and obvious fact?
- Find $E[XY|Y+Z=1 ]$
- Refuting the Anti-Cantor Cranks
- What are imaginary numbers?
- Determine the adjoint of $\tilde Q(x)$ for $\tilde Q(x)u:=(Qu)(x)$ where $Q:U→L^2(Ω,ℝ^d$ is a Hilbert-Schmidt operator and $U$ is a Hilbert space
- Why does this innovative method of subtraction from a third grader always work?
- How do we know that the number $1$ is not equal to the number $-1$?
- What are the Implications of having VΩ as a model for a theory?
- Defining a Galois Field based on primitive element versus polynomial?
- Can't find the relationship between two columns of numbers. Please Help
- Is computer science a branch of mathematics?
- Is there a bijection of $\mathbb{R}^n$ with itself such that the forward map is connected but the inverse is not?
- Identification of a quadrilateral as a trapezoid, rectangle, or square
- Generator of inertia group in function field extension
Popular # Hahtags
second-order-logic
numerical-methods
puzzle
logic
probability
number-theory
winding-number
real-analysis
integration
calculus
complex-analysis
sequences-and-series
proof-writing
set-theory
functions
homotopy-theory
elementary-number-theory
ordinary-differential-equations
circles
derivatives
game-theory
definite-integrals
elementary-set-theory
limits
multivariable-calculus
geometry
algebraic-number-theory
proof-verification
partial-derivative
algebra-precalculus
Popular Questions
- What is the integral of 1/x?
- How many squares actually ARE in this picture? Is this a trick question with no right answer?
- Is a matrix multiplied with its transpose something special?
- What is the difference between independent and mutually exclusive events?
- Visually stunning math concepts which are easy to explain
- taylor series of $\ln(1+x)$?
- How to tell if a set of vectors spans a space?
- Calculus question taking derivative to find horizontal tangent line
- How to determine if a function is one-to-one?
- Determine if vectors are linearly independent
- What does it mean to have a determinant equal to zero?
- Is this Batman equation for real?
- How to find perpendicular vector to another vector?
- How to find mean and median from histogram
- How many sides does a circle have?
This is just the definitions. Distribution $\mu$ is absolute continuous wrt distribution $\nu$ means for any (measurable) set $A$, $\nu(A)=0$ implies $\mu(A)=0$. Does that hold for your examples? No, $A=[3,5]$ has measure zero under $Unif[0,3]$ but 1/2 under $Unif[1,5]$. $\mu$ is singular wrt $\nu$ means for any set $A$, $\mu(A)>0$ implies $\nu(A)=0$. Counterexample for your examples is $A=[1,2]$ (or any subinterval). Visually, the first notion means the support of one distribution is contained in the other. The second notion means the support of one notion is disjoint from the other. You can see neither applies to the pair $Unif[0,3]$, $Unif[1,5]$.