# Tagged Questions

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### Probabilities and random variable problem

Suppose we have a random variable X, and we are given the numerical values of its expectation as well as its s.d. (standard deviation). How can I go about finding the maximum value the probability of ...
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### Generate random variable from series of its expected values E[X], E[X^2], E[X^3], …?

Given a series of all the expected values of a random variable, can we find the random variable itself ?
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### Find the cdf associated with each pdf (NOT transformation)

Find the cdc associated with each pdf: a) f(x) = 3(1-x)^2 , 0 < x < 1 , zero elsewhere b) f(x) = 1/x^2 , -infinity < x < infinity The answers are a) 1-(1-x)^3 , 0 <= x < 1 b) 1 ...
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### Variational problem concerning variances

Let $\phi$ be the family consisting of all random variables $X$ such that $P(X\in [0,1])=1$, $EX=\frac{1}{3}$, $P(X<\frac{1}{4})<\frac{1}{2}$, $P(X>\frac{1}{4})\geq\frac{1}{2}$. Calculate ...
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### Random variable modeling arthroscopic meniscal repair

The below problem is from my introductory stats textbook, the chapter on random variables and probability distributions. I don't even know what's being asked, much less how to answer it. Any clues? ...
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### finding out the probability density of a random process

I have to find out the probability density function of a random process with the following specifications:z(t)= xcos(wt)-ysin(wt) where x and y are two independent gaussian random variables. Now what ...
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### $X,Y$ independent then $X+Y$, $X-Y$ independent as well?

My question is simple: If $X$, $Y$ are independent random variables then $X+Y$, $X-Y$ independent as well?
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### Mean and Variance of Y using Expectation Operator

Let $$Y =\sum_{k=1}^N a_kX_k$$ be the weighted sum of N independent random variables, $X_k, k = 1, ... , N$ , each having mean $\mu _{X_i}$ and variance $\sigma ^2_{X_i}$. The weights $a_k$ ...
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### Expectation of the min of three uniform i.i.d variables [closed]

Let it be T=min(X,Y,Z) where X,Y,Z ~ U(a,b). What is E(T)=?
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### Probability that a five is seen before any of the even numbers are seen

A fair die is repeatedly tossed. What is the probability that a five is seen before any of the even numbers are seen? I have my own solution below and just want someone to verify it. According ...
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### Variance of the sum of sample means

Let $X$ be a random variable with normal distribution with mean $\theta$ and variance $a>0$. Let $Y$ be a random, variable with normal distribution with mean $\theta$ and variance $b>0$. ...
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### Is the set $\limsup\limits_n\{\frac{X_n}{\log(n)}>\frac{1}{\lambda}\}$ equal to $\{\limsup\limits_n\frac{X_n}{\log(n)}>\frac{1}{\lambda}\}$?

Difference between $\limsup\limits_n\{\frac{X_n}{\log(n)}>\frac{1}{\lambda}\}$ and $\{\limsup\limits_n\frac{X_n}{\log(n)}>\frac{1}{\lambda}\}$ are the sets equal ? I think they would ...
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Here's my work for part a. I could use clarification on part b and d. Is part d the same as part a ($E[A_n] = E[Y]$) ? a) $$E[Y_n] = E[\frac{X_n}{2^n}]$$ ($X$'s are iid so...) $$= \frac{E[X]}{2^n} ... 1answer 75 views ### Mean of Piecewise function resting on IID random variables Suppose IID random variables X_t \sim X with support on [0,1] and continuous CDF F(\cdot). I wish to compute the expected value (mean) of the a piecewise function with form$$ \Phi (x,\mu) = ...
There are two independent Gaussian R.Vs: $U:N(-1,1)$ and $V:N(1,1)$ How do I go about finding the PDF of the following transformations? X = U+V T = (U+2V, U-2V) W = U (with 50% chance), V (with ...