0
votes
1answer
8 views

Finding the range from standard deviation and Gaussian Curve

The figure above shows a normal distribution with mean m and standard deviation d, including approximate percents of the distribution corresponding to the six regions shown. Suppose the heights of a ...
0
votes
1answer
30 views

An organization was surveyed with regard to the number of children each member had…

I am studying for my exam and there is no solution for this question. Can anyone provide the correct answers? Thanks. An organization was surveyed with regard to the number of children each member ...
0
votes
0answers
15 views

Can you find a method of moments of Gaussian AR(1)?

This is an exercise from Mathematical Statistics: Basic ideas and Selected topics, Bickel&Doksum, page 141. Gaussian AR(1) model; $X_i = \mu + e_i, i=1, \cdots,n$ $e_i = \beta e_{i-1} ...
0
votes
0answers
24 views

Given two sets, how can I say statistically if they are similar/different

This is a very open ended question. Suppose I have two sets of data samples of the same form, say [item, rating]. Rating is a value on the interval [0,100] and item is a unique identifier given to a ...
0
votes
1answer
37 views

formula to apportion cost of transport among three people in a liftshare

I share lifts with Sed and Awk to work every day. We tally journeys owed on a spreadsheet. A week might look like this: ...
1
vote
1answer
51 views

The Average Speed of an object

I'm pretty sure this has more to do with fundamental Math than Physics and that is why I'm asking this here rather than Physics.SE Imagine some object travelling along a straight path from point $A$ ...
0
votes
0answers
92 views

markov chain - transition matrix - why is this?

I am stuck in this trivial issue: i am given a state for which i need to give a markov chain transition matrix. i couldnot do that and i saw the solution, now i dont understand why solution this is. ...
2
votes
1answer
87 views

X,Y are independent RVs with known characteristic functions. Find P(X+Y=2).

X,Y are independent random variables with the following characteristic functions: $ \phi_X(\theta) = \frac{1}{4}e^{i\theta}+\frac{3}{4}e^{i2\theta} \\ \phi_Y(\theta) = ...
0
votes
0answers
59 views

Define a problem using chernoff bounds

We are preparing this for an exam. Given the division of a plane into a number of regions of different sizes. We would like to find, or guess, which is the biggest region, by doing the following. We ...
7
votes
2answers
267 views

Mean and Median in a Classic River Crossing Problem

Consider the following classic problem: Four people on the west side of a river wish to use their single boat to get to the east side of a river. Each boat ride can hold at most two people, and the ...
4
votes
0answers
428 views

Conditional expectation of the product of two independent random variables

Suppose that $a$ and $b$ are independently distributed random variables, with means; $\mu_a$, $\mu_b$ and variances; $\sigma_{a}^2$, $\sigma_b^2$, respectively. Further, let $c=ab + e$, where $e$ is ...
2
votes
2answers
157 views

Find expectation of conditional random variables

Let $X$ and $Y$ be independent exponential random variables with means 1 and 2 respectively. Let $Z = 2X + Y$. How can I find $E(X|Z)$?
0
votes
1answer
267 views

Find normal random variable from uniform

Suppose $U$ and $V$ are independent random variables with density $f(u)$ and $g(v)$ respectively. The domain of $U$ is the interval $(0, 1)$ and the domain of $V$ is $v > 0$. After the ...
1
vote
1answer
237 views

Find joint density from transformation

I'm trying to learn some tricks for how to find joint densities from transformations, but this problem looks really hard. Any help? Suppose the joint density of continuous random variables $X,Y,Z$ is ...
2
votes
1answer
700 views

Calculating percentage

I'm wondering if my answer for C would be correct and if I was understanding A correctly? I heard drawing venn diagram could help but I'm not sure how to convert the numbers to a diagram. A ...