# Tagged Questions

Questions about maps from a probability space to a measure space which are measurable.

24 views

### Which probability is greater, given minimal info

which probability is greater, given that $X$ and $Y$ are independant, positive random variables? There is also the option that it's impossible to know as we don't have enough information. I'd ...
52 views

### Determine whether a random binary sequence was generated by human or natural process

Given a binary sequence, how can I calculate the quality of the randomness? Following the discovery that Humans cannot consciously generate random numbers sequences, I came across an interesting ...
16 views

40 views

### Transformations of two Laplace distributions resulting in a Laplace distribution

Suppose we have two independent identical random variables $X_1$ and $X_2$ with Laplace distribution \begin{align} f_X(x)=\frac{1}{2b}e^{-\frac{|x|}{b}} \end{align} I am looking for a non-...
2k views

### Assumption of a Random error term in a regression

In one of my recent statistics courses, our teacher introduced the linear regression model. The typical $y=\alpha + \beta X + \epsilon$, where $\epsilon$ is a "random" error term. The teacher then ...
22 views

### Relationship Between $\mathbb{E}$(time) and $\mathbb{E}$(Repetition)

Consider aa Stochastic Process with Expected value of time of occurring =T (less than infinity). Can we deduce that Expected value of number of occurrences until time T is equal to 1?? If not, in ...
27 views

### Expected value and variance of a random variable, defined as the largest of $6$ randomly drawn numbers

Let each of the numbers from $1$ up to $49$ be written on a ball, and let all these balls be contained in a box. From this box, we randomly draw exactly $6$ numbers (without putting them back, so we ...
36 views

### Transformation of random variables that preserves the distribution

Suppose we have a random variable $X$ with distribution $F_X$. Let $X_1$ and $X_2$ be two independent copies of $X$. My question: can we find a transformation $Z=g(X_1,X_2)$ such that the ...
27 views

32 views

### sigma algebra generated by fraction of random variables [closed]

Suppose there are two positive random variables $X$ and $Y$. Is this true that $$\sigma(X/Y)=\sigma(X,Y)?$$ Any help will be appreciated. Thanks a lot.
25 views

27 views

### Joint density function of $T_1,T_2$ and expectation of $E[T_1 ^2 +T_2 ^2 ]$

Given that $T_1,T_2$ are random variables representing the useful life (in hours) of two electrical appliance. The joint probability function of two variables distributed uniformly in the domain ...
32 views

24 views

### Calculate the Covariance of random variables that distribute normally

$X_1$ and $X_2$ are two independent random variables that distribute normally with mean $μ$ and variance $σ^2$. $Y_1 = X_1 + 2X_2$ $Y_2 = X_1 - 2X_2$ Calculate $Cov(Y_1,Y_2)$. Well, I ...
39 views

### Distribution of ages of 3 children in a family

Please consider the following problem: A family has 3 children, creatively named A,B, and C. (a) Discuss intuitively (but clearly) whether the event “A is older than B” is independent of the event “...
44 views

### Probability: finding the expectation of “overlapping events” [duplicate]

Suppose there are 666 coins with 6 different colors in a non-transparent box. 111 of them are white coins. 111 of them are black coins. 111 of them are yellow coins. 111 of them are red coins. 111 of ...
36 views

### Expected number of duplicates

Suppose I have $m$ bins and throw $n\ll m$ balls into the bins uniformly at random. (In my application $n\sim m/\log m.$) What is the expected number of duplicates? In other words, if there are $k_i$ ...
In linear algebra, there is a theorem that states that $\langle v, w \rangle = 0$ implies that $v$ and $w$ are linearly independent. Now let $V$ be a vector space of real-valued random variables on ...
### Finding the density for $\min\{X, Y\}$
Problem: Let $X$ and $Y$ be independent and suppose that each has a $\text{Uniform}(0,1)$ distribution. Let $Z = \min\{X, Y\}$. Find the density $f_Z(z)$ for $Z$. Hint: It might be easier to first ...