I'm told you can do so but I'm struggling to make the connection between the MGF and the probability of the sample space.
2026-04-01 02:01:54.1775008914
How can you use the moment generating function of a random variable to prove that the probability of its sample space is 1?
79 Views Asked by Bumbble Comm https://math.techqa.club/user/bumbble-comm/detail At
1
There are 1 best solutions below
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 MOMENT-GENERATING-FUNCTIONS
- Is it possible to find an upper bound on the moment generating function of $\sqrt{|X|}$, where $X\sim \mathcal{N}(0,1)$?
- Moment Generating Function to Distribution
- moment-generating function for uniform discrete distribution
- Moment Generating Function from Piecewise Constant CDF?
- Variance Derivation of Chi-Squared Distribution
- Finding a PDF from a MGF
- How to prove sample variance has a gamma distribution by using mgf.
- Is $\mathcal{L}_{M}(\Omega, \mathcal{F}, \mathbb{P})$ a linear subspace?
- Let $X$ and $Y$ be independent and identically distributed random variables with moment generating function then $E(\dfrac{e^{tX}}{e^{tY}})$
- Joint Moment Generating Function from Conditional and Marginal Distribution
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?
Unless you have further context here, I don't see why you are proving this; the probability of the sample space being one is an axiom of probability.