# All Questions

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### Using random number generator to draw from population

Suppose X is exponentially distributed, f(x) = e^(x/10)/10. How would you use a random number generator to generate a sample of observations from this population?
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### Markov matrices: finding the initial state vector

I am wondering how can I find an initial state vector for this problem. If the air quality is good one day, it has 95% chance it will be good the next day. If the air quality is bad one day it has ...
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### Probability Strategy

A charity fund-raiser has found that active soliciting gains \$5 contributions with probability .7 and passive soliciting gains \$10 contributions with probability .4. No other contributions are made. ...
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### Why does the group $\mathbb{Z}^d \rtimes \mathbb{Z}^k$ have exponential growth?

I apologize if this is posted on the wrong forum, I was reading this question on MathOverflow which asks about "growth rate of $\mathbb{Z}^2\rtimes_{\sigma} \mathbb{Z}$". The last comment of the ...
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### An simple algebra problem

Could someone check if my algebra is right? If $x_n = \dfrac{1}{a^{a^n}}$ where $a > 1$ and $a$ is natural number, what is $$\lim_{n \to \infty} \frac{|b_{n+1}|}{|b_n|^R}$$? Where $b_n = x_{2n}$ ...
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### Stochastic in finance

I need of a undergraduate guide level to study stochastic process with finances. Starting from a review of probability theory. Eg books, papers or posts. I'll apreciate some help.
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### Derivative Confusion

I am confused about something. In derivation we learnt that; a^x = a^x . lna Now the question that comes to mind is what is the difference when we have: a^3 =
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### how to differentiate a function with square root

Trying to solve $y =7t^4-10 \sqrt {t+\frac{10}{t}}$ I know how to differentiate down to $7(4t^3)- . . .$ and I know a sqrt is equal to $x^.5$ but cannot figure out how to apply that to the rest of ...
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### Finding a Householder matrix for row elimination

I was wondering how to find a Householder matrix such that I could apply it from the right side of a matrix and eliminate values along a row. For example, I have a matrix of the form B = ...
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### For all sets A, B and C, if $A\setminus(B \cup C) = \emptyset$ ; then $A\setminus C\subseteq B$.

For all sets A, B and C, if $A-(B \cup C) = \emptyset$ ; then $A-C\subseteq B$. Is it true? If it is, how to prove it? I think it's true...
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### Sampling from a Normal Distribution

If I am sampling randomly from only the -sigma to +sigma interval of a normal distribution and rejecting all other numbers, does it imply that the probability density changes? If so, by what degree? ...
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### Solution of “quadratic equation” involving functional coefficients.

Suppose I have a "quadratic equation" whose coefficients are functions of the variable to be solved for: $$f(x)x^2+g(x)x+h(x)=0,$$ with $f,g,h\neq 0$. Would it make sense to apply the quadratic ...
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### Convolution product

How can we prove that if $f$ is compactly supported and $g$ is periodic with period $P$ then $f*g$ exists and is also P-periodic ? thanks.
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### How to compute the mean average exponent of the naturals? What is the limit for large numbers?

With a friend I was trying to get an understanding for why the expected gap between primes is logarithmic. With that motivation I tried to express the average exponent of numbers. By average ...
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### More transcendental numbers than natural numbers [duplicate]

Are there any simple proofs that obtain this result? I haven't been able to find one online.
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### keeping c1 continuity in joining several bezier curve

I have some complex curves, I separate the long curves to smallest one to be able to fit them with Bezier curve. However, my Bezier curve has no C1 continuously, if I force C1 continuously, my curves ...