# Tagged Questions

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### Normal Random Variables

Let Z1 and Z2 be independent standard normal random variables. What is the probability that the minimum of Z1 and Z2 will be greater than 1.0? How do I go about this when I have no values? Is the ...
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### If speeds of two cars are Normal RV s, what is the distribution of the distance between them?

The speeds of two cars are random variables that follow $N(\mu_1,\sigma_1)$ and $N(\mu_2,\sigma_2)$ distributions.They start simultaneously. Let X be the distance between them after m hours. (Note ...
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### PDF of X +Y + X* Y, when X and Y are independent Normal [closed]

I have $X,Y$ iid Normals $N(0,\sigma^2)$ What is the distribution of $X+Y+YX$? Thnks a lot!
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### Variance of a Population of Two Indpendent Random Variables

I have a question regarding a problem I'm looking at out of personal curiosity. Here is the basic setup of the problem: There is a population that contains half of type A, and half of type B. The ...
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### Condition on variable to make events independent

where, $$n_1,n_2,...,n_M \sim N\left(0,\frac{N_0}{2}\right)$$ how the condition on n_1 makes the events independent ? what is "n_1=n"
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### Accuracy of a Normal Approximation for a Poisson random variable.

compute bound on accuracy of a normal approximation for a poisson random variable with mean 100? I understand what the question is trying to ask me but I have no idea how to approach it and solve it. ...
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### variance of a random variable

If $X_1, X_2 , ....., X_n$ iid $N(0,1)$ , and $S^2$ was defined as the population standard deviation we are to find the variance of $S^2$ I want to know the distribution in order to find the ...
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### moment generating function technique

If $X$ was a random variable with a distribution $\mathrm{Normal} ( 0, 1 )$, using moment generating function technique we have to show that $Y= X^2$ has the Chi-square distribution with $1$ degree of ...
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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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### Absolute value of the Fourier Transform of Gaussian random variable

Assume you have a normally distributed random variable $x$ with zero mean $\mu$ and standard deviation $\sigma$. Now you take the Fourier transform of it. The resulting complex random variable ...
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### Are any linear combination of normal random variables, normally distributed?

It is easy to show that if we have n independent normally distributed random variables, then a linear combination fo them ar normally distributed. It is also said that if (x1,x2,..,xn) is ...
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### Product of standard normal and uniform random variable

I'm trying to find the PDF of the product of two random variables by first finding the CDF. I don't know where I'm going wrong. Let $X\sim N(0,1)$ and $Y\sim Uniform\{-1,1\}$ and let $Z = XY$, then: ...
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### help with Borel Cantelli lemma

There is a sequence of random variables $X_1,X_2,...$ For each i $X_i$ ~ $Normal(0,1)$ Is $\frac{X_n}{n} \rightarrow 0$ almost surely? Is $\frac{X_n}{lnn} \rightarrow 0$ almost ...
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### How to generate normally distributed random numbers? [duplicate]

Is there any function that can generate normally distributed random numbers?
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### Sampling distribution with large sample size

As the sample size $n$ of a sampling distribution of sample means increases, the distribution becomes more normal. But if $n$ were the same size as the (finite) population, the "sampling" distribution ...
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### Probability question of independent random varaibles

Let $X\sim \mathcal{N}(6,1)$ and $Y\sim\mathcal{N}(7,1)$ be two independent normal variables. Find $Pr(X>Y)$. the answer is $0.2389$ but I do not know how to do it.
I have a question regarding a property of the error function. Is $k\cdot\text{erfc}(-x) = 1-k\cdot\text{erfc}(x)$ for all real $x$ for any $k$?