I am stucking on this problem from days, I need help, if anyone could help me. I have $Y=\log(1+X)$ with $X$ that follows an exponential distribution, I would understand which is the $Y$ distribution, is $Y$ also exponential?
Thank you in advance
2026-03-31 12:10:17.1774959017
Exponential distribution?
83 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-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 LOGARITHMS
- Confirmation of Proof: $\forall n \in \mathbb{N}, \ \pi (n) \geqslant \frac{\log n}{2\log 2}$
- Extracting the S from formula
- How to prove the following inequality (log)
- Rewriting $(\log_{11}5)/(\log_{11} 15)$
- How to solve this equation with $x$ to a logarithmic power?
- Show that $\frac{1}{k}-\ln\left(\frac{k+1}{k}\right)$ is bounded by $\frac{1}{k^2}$
- Why do we add 1 to logarithms to get number of digits?
- Is my method correct for to prove $a^{\log_b c} = c^{\log_b a}$?
- How to prove the inequality $\frac{1}{n}+\frac{1}{n+1}+\cdots+\frac{1}{2n-1}\geq \log (2)$?
- Unusual Logarithm Problem
Related Questions in DENSITY-FUNCTION
- Find probability density function for $\varepsilon \cdot X$.
- Density distribution of random walkers in a unit sphere with an absorbing boundary
- Find the density function of the sum $(X,X+Y)$.
- Conditional density function with gamma and Poisson distribution
- Variance of a set of quaternions?
- Generate uniformly distributed points in n-dimensional sphere
- probability density function-functions of random variables
- joint probability density function for $ X = \sqrt(V) \cdot cos(\Phi) $ and $ Y = \sqrt(V) \cdot sin(\Phi) $
- Joint probability density function of $X$ and $\frac{Y}{X}$
- Equivalent ways of writing Kullback-Leibler divergence
Related Questions in EXPONENTIAL-DISTRIBUTION
- Comparing Exponentials of different rates
- Find probability density function for $\varepsilon \cdot X$.
- What is $\mathbb{E}[X\wedge Y|X]$, where $X,Y$ are independent and $\mathrm{Exp}(\lambda)$- distributed?
- Restaurant sending orders every 5 minutes on average
- How to estimate Reliability function in Weibull by the failure rate
- exponential distribution of an exponential variable
- Joint probability density function of $X$ and $\frac{Y}{X}$
- distribution of Z=X+Y
- Probability of two randomly selected leaves of a tree to be connected only at the root
- Reasonable/unreasonable exponentially distributed interarrival (service) times
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?
No. If $X\sim\operatorname{Exp}(\lambda)$, the CDF of $Y$ is$$P(Y\le y)=P(X\le\exp y-1)=1-\exp(-\lambda(\exp y-1))$$for $y\ge0$. This is a Gompertz distribution with $\eta=\lambda,\,b=1$.