Tagged Questions
2
votes
1answer
65 views
Joint distributions for uncorrelated varibles
Can someone think of joint distribution of random variables X, Y such that the following three
conditions are satisfied:
$E[X] = 1$,
$E[Y] = 1$, and
$E[XY] = 0$?
A friend of mine asked me this, ...
0
votes
0answers
47 views
the expected value of your gain
You flip a coin and if it is a head I pay you 1 pound but if it is a tail you pay me 2 pounds. You have 50 pounds and you stop when you spend all of your money or you flipped coin 100 times. What is ...
0
votes
2answers
250 views
Given a table defining the joint probabilities, how do I calculate certain parameters of the marginal distributions?
The number of items sold on any one day in the traditional shop is a random variable X and the corresponding number of items sold via the Internet is a random variable Y. The joint distribution of X ...
1
vote
1answer
119 views
How to find Coefficient of Variation with E(X), E(X^2) and sample size?
Given E(X), E(X^2) and sample size. How do I find Coefficient of Variation?
Variance = E(X^2) - E(X)^2
sd = square root of variance
Coefficient of Variation = sd / E(X)
however, with the values ...
2
votes
0answers
55 views
Finding correlation coefficient
if I have A and B with the following known variables:
with $E[A]$, $E[B]$ , $\sigma_{A}$ , $\sigma_B$
and correlation coefficient: $\rho_{AB}$ (assign numbers if you like)
Say: $C=0.6A+0.4B$
Then ...
0
votes
0answers
17 views
Expected value (Chi-Squared) [duplicate]
Possible Duplicate:
Why is sample standard deviation a biased estimator of $\sigma$?
Let $X_1, X_2, X_3 \sim N(0, d^2)$ and $T = X_1^2 + X_2^2 + X_3^2.$
T is chi-squared distributed, ...
2
votes
1answer
92 views
Conditional Expectation / Estimator Confusion
Let $X_1, X_2, X_3 \sim N(0, d^2)$ and $T = X_1^2 + X_2^2 + X_3^2.$
I have an estimator for $d$, $$\hat{d} = \frac{\sqrt{T\ 2\pi}}{4},$$
and another estimator for $d$, $$\tilde{d} = \frac{1}{3} ...
1
vote
1answer
272 views
Sum of Gamma distributions
The lifetime of a particular brand of batteries is known to have a gamma distribution. Tests on a large sample of these batteries show a mean lifetime of 480 hours and a standard deviation of 96 ...
1
vote
1answer
107 views
Show that Y/Z does not have finite expectation
The unit interval (0, 1) is divided into two sub-intervals by picking a
point at random from inside the interval. Denoting by Y and Z the
lengths of the longer and the shorter sub-intervals ...
3
votes
1answer
121 views
Find probability and expectation
18 boys and 2 girls are made to stand in a line in a random order.Let $X$ be the number of boys standing in between the girls .Find $P[X=5]$ and $E[X]$. I proceed in this way:
Note that ...
1
vote
1answer
133 views
Expected number of failures preceding the first success
I am a beginner in statistics and probability. I have a question that says
What is the expected number of failures preceding the first success in an infinite series of independent trials with the ...
1
vote
1answer
130 views
Determining the expected number of accident-free days per year in a city
If a city has an average of two accidents per day, how many accident-free days do you expect in a year?
0
votes
1answer
900 views
1
vote
1answer
141 views
Some doubts about conditional expectation
Suppose I have two random variable $X_t\sim NID(0,1)$ and $Y_t\sim NID(0,4)$ and $Cov(X_t,Y_t)=2$ .
Consider the random variable $Z_t = X_t + Y_t + Y_tX_t$.
$E(Z_t) = E(X_t)+E(Y_t X_t)+E(Y_t) = 0 + ...
5
votes
1answer
342 views
Expected value and variance of arithmetic mean of random variables
The question is
Let $X_1,...,X_n$ be drawn iid from $Beta(0.1,0.5)$. Let $\bar{X} = \frac{1}{n}\sum^n_{i=1} X_i$.
a) Derive $\mathbb{E}(\bar{X})$ and $\mathbb{V}(\bar{X})$
I know how to ...
4
votes
2answers
667 views
Using control variates & antithetic method with Monte Carlo
Supposing $g(x)=\sqrt[3]{x}$, I want to calculate the expected value of g, $E(\sqrt[3]{x})$, using Monte Carlo method, by generating $x_i$ from a Weibull distribution with parameters $(1,5)$.
After ...
0
votes
1answer
101 views
Why z=f(x) does not imply E[z]=f(E[x]) when f is not linear?
Why $z=f(x)$ does not imply $E[z]=f(E[x])$ when f is not linear?
I can give an example, but I couldn't derive the general form.
Let $z = {x^2}$
Let $g(x)$ be the pdf of $x$. Then:
$ E\left[ z ...
5
votes
3answers
5k views
Find expected value using cdf
I'm going to start out by saying this is a homework problem straight out of the book. I have spent a couple hours looking up how to find expected values and have determined I understand nothing.
...
