Is it true that: $$E_t\bigg[\dfrac{exp(f(x))}{E_t\big[exp(f(x))\big]} log(E_t(exp(f(x))))\bigg] = log(E_t(exp(f(x)))),$$ where $E_t$ is the expectation given information in $t$?
Thanks a lot for your help!
2026-04-05 07:49:08.1775375348
Expectations, Logarithm, and Exponents
34 Views Asked by Bumbble Comm https://math.techqa.club/user/bumbble-comm/detail AtRelated 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 EXPONENTIAL-FUNCTION
- How to solve the exponential equation $e^{a+bx}+e^{c+dx}=1$?
- derive the expectation of exponential function $e^{-\left\Vert \mathbf{x} - V\mathbf{x}+\mathbf{a}\right\Vert^2}$ or its upper bound
- How do you calculate the horizontal asymptote for a declining exponential?
- Intersection points of $2^x$ and $x^2$
- Integrate exponential over shifted square root
- Unusual Logarithm Problem
- $f'(x)=af(x) \Rightarrow f(x)=e^{ax} f(0)$
- How long will it take the average person to finish a test with $X$ questions.
- The equation $e^{x^3-x} - 2 = 0$ has solutions...
- Solve for the value of k for $(1+\frac{e^k}{e^k+1})^n$
Related Questions in EXPECTED-VALUE
- Show that $\operatorname{Cov}(X,X^2)=0$ if X is a continuous random variable with symmetric distribution around the origin
- prove that $E(Y) = 0$ if $X$ is a random variable and $Y = x- E(x)$
- Limit of the expectation in Galton-Watson-process using a Martingale
- Determine if an Estimator is Biased (Unusual Expectation Expression)
- Why are negative constants removed from variance?
- How to find $\mathbb{E}(X\mid\mathbf{1}_{X<Y})$ where $X,Y$ are i.i.d exponential variables?
- $X_1,X_2,X_3 \sim^{\text{i.i.d}} R(0,1)$. Find $E(\frac{X_1+X_2}{X_1+X_2+X_3})$
- How to calculate the conditional mean of $E(X\mid X<Y)$?
- Let X be a geometric random variable, show that $E[X(X-1)...(X-r+1)] = \frac{r!(1-p)^r}{p^r}$
- Taylor expansion of expectation in financial modelling problem
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?