Linear Combination Puns

Given means and variances of a finite set of random variables find variance of their linear combination.

First I need to scale each variable, and it means just multiplying the mean and the variance by corresponding scalar.

Then mean of a sum is a sum of means.

Can you explain to me how to find covariance?

I try case with two RVs and variance should be var_1+var_2 +2*covariance, right?

I get an answer order of magnitude off expected value. What might I do wrong?

I understand that gcd has to divide every linear combination of those numbers and with the help of extended Euclidean algo that it can always be expressed as a linear combination, intuitively it could be the smallest one. But why any other common divisor can't be written as a linear combination, since it divides all combinations?

Some creative types are “airheads” or just plain aloof, having no concrete knowledge on any one particular subject. Some “book-smart” people do not have a single creative bone in their body and cannot view something in a way other than how it can be explained logically to them.

So, I'm homeschooled and am currently doing a trig/pre calculus class. I've had issues with this program before, but the information on this page ( https://www.ck12.org/user:agvicmv3czexmebnbwfpbc5jb20./book/ep-trigonometry-second-edition/r1/section/3.7/ ) is making no sense to me. It feels like it's throwing so much new information at me while I've barely even figured out the stuff before. I've tried looking around for the stuff on this page, like on Khan Academy and other places, but I've had no luck finding anything. Does anyone know of any better websites that teach the stuff on this page more clearly?

what is the difference between linear combination ,to be exact affine combination , and slope- intercept form of line ,especially in terms of coefficents ,I mean in slope-intercept form of line the coefficient slope is the rate of change of the line but in linear combination it isn't the case, is it ? And they have similar expression ,so what's the difference between them ,especially in term of coefficients?

I'll be attending UChicago this year as an exchange student and I am trying to make the most out of this year..

I am particularly interested in gaining the quantitative skills I need for economics/social research (I am an Econ Major in my home university), thereby I am currently thinking of the following:

Quarter 1: SSI + Linear Algebra + Statistical Models and Methods Quarter 2: SSI + Applied Regression Analysis + Econometrics Quarter 3: SSI + Applied Microeconometrics

I am allowed to take up to 4 courses per quarter thereby I'll still have to pick additional courses. I am concerned, however, that the workload might be very stressful given the quantitative nature of all the course, so I really wanna know your opinion about that as well as about any better ideas you might have on how to spend my time during this year..

My background:

I've taken very little calculus (my college is really bad :v) but I have recently re-built my skills using MIT's Single Variable Calculus course on the opencoursewar (I do all the PSets and Exams), and I'll be probably done with the differential calculus portion of the Multivariable Class by the beginning of the quarter.

My exposure to linear algebra is limited, I've mainly acquired the skills needed for Introductory Multivariable calculus (there's a module at the beginning of the MIT's multivariable class) yet I haven't done any dedicated linear algebra work before..

Stat classes are extremely bad at my college as well, so while some recommend that I skip the stat class and jump directly to Econometrics, I really want to have a good foundation in statistics because I am very into research/analysis as a professional.

Why am I not planning to take Econ theory classes? Because I think it's better to acquire the tools which will enable me to empirically work using models, so that when I study them later I am able to do a lot of applications (It's just a matter of having limited time at UChicago), but please let me know your thoughts on that as well..

Thanks!

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Say I have a set of workers and wish to appoint them to different groups, while minimizing costs. The optimization itself is not of interest here.

Below is an MVE in which I try to construct a variable that indicates which of the possible combinations of workers is chosen.

>Example: If "Sigrid", "Timo" and "Maria" are chosen, the combinations-variable "Sigrid_Timo_Maria" should be == 1.

My try at this problem is in the code block below the comment "# set up indicator for combination".

import itertools
import pulp
groups = ["A","B","C"]
workers = ["Sigrid","Timo","Delf","Maria","Lisa"]
hours = [1,1,1,1,1]
worker_hours = dict(zip(workers, hours))
group_worker = [(group, worker) for group in groups for worker in workers]
worker_combinations = [i for i in itertools.combinations(workers,len(groups))]

# intiate linear programming-Variables:

worker_indicator_lp = pulp.LpVariable.dicts("Chosen",workers,0,cat='Binary')
group_worker_amount_lp = pulp.LpVariable.dicts("Amount",group_worker,0,cat='Integer')
group_worker_indicator_lp = pulp.LpVariable.dicts('Chosen',group_worker,0,cat="Binary")
worker_combination_indicator_lp = pulp.LpVariable.dicts('Combination_Chosen',worker_combinations,0,cat="Binary")
# initiate problem

prob = pulp.LpProblem("Diet Problem",pulp.LpMinimize)
# set up constraints
prob += pulp.lpSum([worker_hours[worker] * group_worker_amount_lp[group,worker] for group in groups for worker in workers])
prob += pulp.lpSum([worker_hours[worker] * group_worker_amount_lp[group,worker] for group in groups for worker in workers]) >= 60

# each worker only in one group

for worker in workers:
    prob += pulp.lpSum([group_worker_indicator_lp[group, worker] for group in groups]) <= 1

# set up indicator for worker-group

for worker in workers:
    for group in groups:
        prob += group_worker_amount_lp[group,worker] >= group_worker_indicator_lp[group,worker] * 0.0001
        prob += group_worker_amount_lp[group,worker] <= group_worker_indicator_lp[group,worker] * 1e4

# set up indicator for worker
for worker in workers:
        prob += pulp.lpSum([group_worker_amount_lp[group,worker] for group in groups]) >= worker_indicator_lp[worker] * 0.0001
        prob += pulp.lpSum([group_worker_amount_lp[group,worker] for group in groups]) <= worker_indicator_lp[worker] * 1e10

# 

Don’t let math work stress you, get help today. I offer help in the following categories:

· Statistics

· Algebra

· Calculus

· Linear Algebra

· Combinations

· Geometry

· Online Classes

· Probability

· Differential Equations

· Number Theory

· Quizzes, Tests, Exams, and Homework

Guaranteed 90+ Grade. Reach me on email: andycookee@gmail.com Discord Andywriters#7925