Tagged Questions

16 views

Stat problem help me! [on hold]

Hello! I got a problem when I was solving stat problem. I solved by(c), but after that, I found it hard to solve. Can you guys help me or give me a hint? Thank you anyway!
28 views

Ratio of Gamma random variables

If $X_i$, $i=1,2$ are independent gamma$(\alpha_i,1)$ random variables, find the distribution of $\frac{X_1}{X_1+X_2}$ and $\frac{X_2}{X_1+X_2}$. Attempt: Let $Y_1 = \frac{X_1}{X_1+X_2}$ and ...
21 views

Finding distribution of random variable if X is exponential $(1)$

Let X be an exponential (1) random variable, and define Y to be the integer part of X+1, that is $\hspace{15mm}Y=i+1$ if and only if $\hspace{5mm}i \leq X \leq i+1, i = 0,1,2,...$. Find the ...
22 views

Correlation and First Order Stochastic Dominance

Suppose we have a random variable $X \sim [0,1]$ with a continuous distribution $F_X(x)$. Suppose $I \in \left\{0,1\right\}$ is a discrete random variable with $\text{Prob}(I=1 \ | \ X=x)$ strictly ...
11 views

Percentages in Normal Distribution

A statistics problem involves: Lengths of a certain type of carrot have a normal distribution with mean 14.2 cm and standard deviation 3.6 cm. (i) 8% of carrots are shorter than c cm. Find the value ...
33 views

Expected Value on code

I'm trying to figure out the expected number of times this algorithm will print. I'm stuck on how to go about doing so. I used an indicator variable to keep track of the number of print statements ...
33 views

Using the inverse Gaussian integral to find percentiles

I need some help with the following: Let $$R=\mu+\sigma*\epsilon \hspace{1cm} \epsilon \sim N(0,1)$$ I want to argue that $$\mu + \sigma*\Phi^{-1}(u)$$ are the percentiles of the model when ...
20 views

Generating random variables with complicated probability distribution functions

I have an interesting question I need to solve, and as much as I try, I cannot wrap my head around it. Given a postive random variable X with p.d.f. ...
24 views

Stat problem! Why is this? [duplicate]

This is a statistics problem. although this is not a problem which needs an answer, I want to know the reason Why this is right. Can you guys help me ? Thanks in advance!
33 views

Joint density of $X_1^2+X_2^2\ \text{and} X_2,\ X_i\sim N(0,1)$

Let $X_1$ and $X_2$ be iid with a common standard normal distribution. I am looking to find the joint pdf of $Y_1 =X_1^2 +X_2^2$ and $Y_2=X_2$. I know i can use a straight transformation argument but ...
30 views

Question I couldn't identify to solve this distribution [closed]

A couple decides to have 3 children.If none of them is a girl,they will try again,and if they still don't get a girl,they will try again and continues so on.If X is the number of children,the couple ...
30 views

Proving consequence of $\operatorname{var}(X)+\operatorname{var}(Y)=\operatorname{var}(X+Y)$

How to prove that if $\operatorname{var}(X)+\operatorname{var}(Y)=\operatorname{var}(X+Y)$, then $X$ and $Y$ are independent?
13 views

Related to chi-squared functions

I'm finding difficulty in finding what type of function it is in continuous distributions in probability.Mainly how can i identify whether a function is chi-squared or not?
16 views

Differential Equation for brownian bridge?

For the brownian motion, we know that probability density of the particle's position at time $t$, $\rho(x,t)$ satisfies the diffusion equation pde: $\partial_t \rho = d \; \partial_x^2 \rho$. Is ...
18 views

Finding $a_n, b_n$ so that a sequence converges in distribution to a nondegenerate random variable.

Now, $X_1, X_2,\dots$ are iid with the same distribution as the chi-squared distribution with one degree of freedom. Find $a_n$ and $b_n$ so that $a_n \left( \max_{1 \leq i \leq n} X_i - b_n \right)$ ...
13 views

26 views

Distribution of the sample variance of n iid exponential variables

I have to check some properties of an estimator, but I can't find its distribution. Let $X_1,...,X_n$ be independent identically distributed exponential variables with parameter $\theta$, i.e. ...
23 views

Poisson distribution equation

This is probably a very simple and silly question to ask, but I just don't understand the steps for b). I don't quite understand where the negative (-) sign came from? Could somebody please shed some ...
55 views

Given a CDF, find P(-.5<X<.5)

Given the following CDF: \begin{equation*} F(x)= \left\{ \begin{array}{lr} 0 & x<-1, \\ \frac{x+2}{4} & -1 \leq x < 1 \\ 1 & x \leq 1 \end{array} \right. \end{equation*} Compute ...
24 views

Hypergeometric RV - what is the sample/population?

An instructor who taught two sections of engineering statistics last term, the first with 20 students and the second with 30, decided to assign a term project. After all projects had been turned in, ...