Tagged Questions
2
votes
2answers
7 views
Decomposition of exponential random variable
I know that sum of independent Exponential random variables follows Gamma distribution.
But
Is it possible to decompose ...
1
vote
2answers
30 views
A probability problem on limit theorem (!)
Each of the 300 workers of a factory takes his lunch in one of the three competing restaurants (equally likely, so with probability $1/3$). How many seats should each restaurants have so that, on ...
1
vote
2answers
70 views
A basic doubt on a probability problem [on hold]
Suppose we have a random variable $X$ with mean $\mu$ such that the probability $P(|X-\mu| > \delta)$ which is a function of $\delta(>0)$ does not have any local minima/maxima. What is the ...
0
votes
1answer
25 views
Mixed cumulative distribution [picture added]
Since $F(x)=pF_d(x)+(1-p)F_c(x)$, so $p=0.3$?
I wonder if there is no more information except $F(x)$'s graph then how we can find $p$?
0
votes
0answers
22 views
Chebyshev inequality and Central limit theorem gives different answer
Let $X_i$ be i.i.d random variables each with mean $\mu$ and variance $\sigma^2$. let $S_n=\sum_{i=1}^{n}X_i$ and $Z_n=\frac{S_n -n\mu}{\sigma\sqrt{n}}$. Now for the probability $P(|Z_n|<k);k=2$ I ...
0
votes
1answer
19 views
Getting two answers using central limit and weak law of large numbers
Let $X_i$ be i.i.d random variables each with mean 1. let $S_n=\sum_{i=1}^{n}X_i$. I have to calculate the probability $P(S_n \leq n)$ as $n$ tends to $\infty$. Now using central limit theorem I am ...
0
votes
0answers
11 views
Equivalence random variables
Under which conditions we can say that 2 random variables are equal/equivalent?
More specifically, I have D a random variable, and $(DR_i, 0 \leq i \leq n)$ a sequence of random variables such that:
...
0
votes
1answer
17 views
A basic question on poisson random variable
Given a Poisson random variable $X$ with parameter $\lambda$, I want to write $X=X_1+X_2$ where $X_i$s are independent Poisson random variables with parameter $\lambda_i$s such that $\lambda=\lambda_1 ...
0
votes
0answers
29 views
Joint probability mass function $f$ of $2$ random variables.
Given $\Omega$={$20, 21, ..., 49$}, $P(i)=\begin{cases}0.05, & \text{if $20<=i<=29$} \\0.03, & \text{if $30<=i<=39$} \\0.02, & \text{if $40<=i<=49$}\end{cases}$
The ...
1
vote
0answers
33 views
Probability for taking out same note from a box with n notes
In a box there are n numbered notes ordered from 1 to n. We are taking out note after note randomly and insert the note back to the box. Let $X$ be the number of chosen notes in the experiment.
...
0
votes
1answer
28 views
Finding the probability density function of one random variable in multiple random variable
The question looks like this, where fx is equal to this:
$f(x) = exp(-(1/2(1 - \rho^2 - \gamma^2))(1-\gamma^2)x_1^2 + x_2^2 + (1-\rho^2)x_3^2 -2\rho x_1 x_2 +2 \rho \gamma x_1 x_3 -2 \gamma x_2 ...
3
votes
2answers
54 views
special sum of binomials distributions
Let $X$ be a random variable. Let $X_p$ be distributed as a Binomial distribution with number of outcomes $X$ and probability $p$, i.e. $Bin(p, X)$. Consider the random variable,
$$
Y = X_p + X_{1-p}.
...
1
vote
1answer
25 views
joint probability distribution of one discrete, one continuous random variable
This is a problem on the joint distribution of a discrete and a continuous random variable.
Kitty Oil Co. has decided to drill for oil in 10 different locations; the cost of
drilling at each ...
1
vote
0answers
15 views
Hypothesis testing for two exponential samples
I'm trying to solve the following exercise from an introductory statistics textbook:
Let $X_1, \dots , X_m$ denote a random sample from the exponential density with mean $\theta_1$ and
let $Y_1 ...
0
votes
1answer
21 views
Finding variance .
Suppose that $f : [0, 1] → [0, 1]$ and we wish to estimate
$$I = \int_{0}^{1} f(x) dx$$
Using the hit-and-miss method, we obtain the estimate
$$\hat I_{HM}=\frac{1}{n}\sum_{i=1}^{n}X_i$$
where ...
