# Tagged Questions

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### suppose x follows a distribution with density function: f(x)=C*abs(x-2), 0 =<x=<3; f(x)=0 otherwise.

suppose x follows a distribution with density function: f(x)=C*|x-2|, 0 <=x<=3; f(x)=0 otherwise. find the cumulative distribution function of F(x) for 2<=x<=3 Find the Median of the ...
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### Distribution of $U=\frac{X}{\| X \|}$ and $R^2 = \| X \|^2$ where $X=(X_1, \dots , X_n)$, $X_1, \dots, X_n \sim$ N(0,1) i.i.d. Independence?

I have the following problem: Let $X=(X_1, \dots , X_n)$, $X_1, \dots, X_n \sim N(0,1)$ i.i.d. What is the distribution of $U=\frac{X}{\| X \|}$ and $R^2 = \| X \|^2$. Are $U$ and $R^2$ independent? ...
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### Statistics - Approximating Poisson Distribution

Y, the number of accidents per year at a given intersection, is assumed to have a Poisson distribution. Over the past few years, an average of 36 accidents per year have occurred at this intersection. ...
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### Two dependent random variables with standard normal distribution and zero covariance

I need to find two dependent random variables with standard normal distribution, but with zero covariance. It is easy too find just two dependent random variables with such a distribution (...
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### Random var. Y with pdf $f_Y(y) = 4y^3$. Show that $-2\ln (Y^4)$ ~ $X_{(2)}^2$.

Let Y be a random variable which has pdf $$f_Y(y) = \begin{cases}4y^3, & 0 < y < 1, \\ 0, &\text{elsewhere}.\end{cases}$$ Show that $-2 \ln (Y^4)$ ~ $X_{(2)}^2$. Could anyone get me ...
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### Help for $U = T^2$ has an $F$ distribution with 1 numerator and $v$ denominator degrees of freedom.

If $T$ has a $t$ distribution with $v$ degrees of freedom, then $U = T^2$ has an $F$ distribution with 1 numerator and $v$ denominator degrees of freedom. First, I set $$T = \frac{Z}{\sqrt(W/v)}$$, ...
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### A conditional probabilty question.

Question: $8$ identical balls are randomly distributed into $8$ boxes. Given first box and second box are not both empty, find the probability that first box is not empty? $A:=$ B1 is not ...
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### Joint PDF of independent and identically distributed random variables [duplicate]

Let $X_1$, $X_2$and $X_3$ be independent and identically distributed random variables with uniform distribution between $[0,1]$. What is $P[X_1+X_2\leq X_3]$?
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### Probability of getting 50 heads is equal to the probability of getting 51 heads

$100$ coins are tossed. Probability of getting $50$ heads is equal to the probability of getting $51$ heads.that probabiity is $.....?$ My TRY i gave a lot time to this problem.but i am very confused ...
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### Distribution function and its concavity

Let $\gamma$ be a parameter which is $0<\gamma<4$. Is the following distribution function concave $$F(x)=1-x^{-\gamma}$$
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### Standard deviation / Bell Shaped Distribution

In a forest, it is known that the circumference of 10 year old oak trees when measured three feet above the ground is 20 inches with a standard deviation of 4.5 inches. It is also known that these ...
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### Pareto distribution and matrix

I am wondering if there are any bounds are known on the eigenvalues of random matrix whose entries are with Pareto distribution? Thank you.
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### Prove that there exists a matrix with no monochromatic sub-matrix

There seemed to be a mistake in the question, so it was edited (my answer is correct). A matrix is monochromatic if it's built from only $0$'s or only $1$'s. Prove that for every $n,k$ such that ...
### Please explain to me why the Expected Value is $E[X] = \int_{-\infty}^{\infty} x f_X(x) dx$
For probability density functions (at least for the normal distribution and beta distribution) it holds that the expected value is given by $E[X] = \int_{-\infty}^{\infty} x f_X(x) \, dx$. I have ...