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Mathematics : Recent Questions and Answers (Page 57)

Find answers to your questions about Mathematics or help others by answering their Mathematics questions.

Characteristic function of random variable is always integrable

Let $X$ be a random variable and let $phi$ be the characteristic function of $X$ . Is the integration of $|phi|$ over $mathbb R$ always...

Asked on 12/03/2021 by Shreya Chauhan

1 answer

Invariant $SU(3)$ subgroup for ${bf 8}$ in ${bf 3}^* otimes {bf 3} ={bf 1} oplus {bf 8}$

This question concerns finding an invariant subgroup of a total group $G$. Warm-Up Toy Example (which I already solved): Let us take $G=SU(2)$ as a special unitary group....

Asked on 12/03/2021 by annie marie cœur

1 answer

Proof that a continuous function with continuous right derivatives is differentiable.

I am looking at the proof given on this question given by "23rd". Continuous right derivative implies differentiability I asked in a comment a question about 5 months ago,...

Asked on 12/03/2021

1 answer

Finding the volume when a parabola is rotated about the line $y = 4$.

Problem: Find the volume generated by revolving the region bounded below by theparabola $y = 3x^2 + 1$ and above by the line $y = 4$ about...

Asked on 12/03/2021

1 answer

Differential equation, modulus signs in solution?

Question: Find the equation of the curve with gradient $frac{dy}{dx}=frac{y+1}{x^2-1}$ that passes through $(-3,1)$. So I integrated both sides with respect to $x$ which gave me...

Asked on 12/03/2021 by Refnom95

2 answer

Consider the sequence where $a_1>0$, $ka_n>a_{n+1}$ and $0<k<1$. Can we say it converges?

I could get that $a_1>k^n a_1 > a_{n+1}$ and therefore $0geqlim a_n$ But I can't find a lower bound for the squeeze theorem or something about monotonicity. Any...

Asked on 12/03/2021 by oek Cafu

1 answer

In a Reflexive banach space, given a closed convex set $C$ and some point $y$, there is a point in $C$, of minimal distance to $y$

In a Reflexive space, given a closed convex set $C$ and some point $y$, there is a point in $C$, of minimal distance to $y$ All...

Asked on 12/03/2021

2 answer

Ball / Urn question with a twist

I am trying to answer questions like: We select, with replacement, $20$ balls from an urn holding $30$ numbered balls. What is the probability that...

Asked on 12/03/2021 by user109387

1 answer

How to prove $phi'(t)1_{Omega_t}(w)$ is measurable?

I need help or any hint in the next exercise: Let $(Omega,mathcal{F},mu)$ be a $sigma-$finite measurable space and let $f:Omegato mathbb{R}$ be a measurable function. Let ...

Asked on 12/03/2021 by czzzzzzz

1 answer

Using characteristic functions to determine distribution of sum of independent normal random variables.

There is a bijective correspondence between characteristic functions and probability distributions. It is stated in Probability Theory by Durrett that from this fact it follows readily that given independent normal...

Asked on 12/03/2021 by JKEG

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