u/ilikemychem

I have an exam coming up, and the solutions manuals are pretty terrible, which wouldn't be an issue if the professor also wasn't. But I essentially have to relearn the entire course on my own, and it is not going well... Here's my question:

https://preview.redd.it/mvgr1g4k2ijh1.png?width=1237&format=png&auto=webp&s=396cbeccea606a46e8cc1624557d6d2a43dfe970

So I tried splitting it up as follows (P{X(1)=0, Y(1)=1, X(2)=0, Z(2)=1}+P{X(1)=0, Y(1)=1, X(2)=1, Z(2)=0}+P{X(1)=1, Y(1)=0, X(2)=0, Z(2)=1}+P{X(1)=1, Y(1)=0, X(2)=1, Z(2)=0})/P{Po(4)=1}

But after that I think I'm doing something wrong, because I get each of the terms in the numerator to 2/e^(2) and the final probability to the same. The solutions say it's 1/e.

Okay, so. I have an upcoming exam on statistical inference where the McNemar's test might come up, and from the way I understand it you simply compare the cross-correlation probability thing with the chi squared for the signficance level and degrees of freedom. Though one formula I've found looks different from the one I was given and I do NOT get it.

I have this table:

2nd A	2nd D
1st A	794
1st D	86

for α=0.01. The solution then computes X^(2)=(150-86)^(2)/(150+86)=17.35 and state that its square root is greater than 4 and thus we can reject H_0. Why the square root???? And why 4????

And then I found another formula that just compares it to chi^(2)_{(2-1)(2-1)}(0.01) but that one would be X^(2)=(|150-86|-1)^(2)/(150+86). What's with the 1????

H e l p

EDIT: I figured out the X^(2)=(|150-86|-1)^(2)/(150+86) part and that it's meant for when the denominator is less than 25. I still don't know where they're getting square root of 4 in the first method, though.

Help with this question please!

"Find the autocorrelation function R_X(s, t) of the process X(t) = √(2) A cos(U t+ Θ) for t ∈ R, where A, U and Θ are independent random variables with A standard normal distributed, U uniformly distributed over the interval [0, 1] and Θ uniformly distributed over the interval [0, π].
"

Hi, I am taking a course on ordinary differential equations and mathematical modelling, and I am a bit confused about a new (?) way of computing eigenvalues.

My teacher has been computing them a lot lately from the vector field f(x,y)=(func1,func2) and then deriving that so Df(x,y)=

f'_x(func1)	f'_x(func2)
f'_y(func1)	f'_y(func2)

and then setting the eigenvalues to f'_x(func1) and f'_y(func2). Am I misunderstanding what he is doing and that is not in fact it at all, or is this a special method when working with initial value problems or something else I do not understand?

[SOLVED]

import numpy as np
from scipy.integrate import solve_ivp
import matplotlib.pyplot as plt

#Definiera paremeter-sets.
sets=[(1,0.5,0.4,9.8,3),(2,0.6,0.5,19.6,15)]
epsilon=1e-6

print (sets)

#Definiera ODE.
def ode(t, v, m, mu_s, mu_k, N, F_0):
    v=v[0]
    
    #kinetisk friktion
    if abs(v)>epsilon:
        v_dot=(F_0-mu_k*N*np.sign(v))/m
        
    #statisk friktion
    else:
        if abs(F_0)<=mu_s*N:
            v_dot=F_0
        else:
            v_dot=(F_0-mu_k*N*np.sign(F_0))/m
    return [v_dot]

def solve_ode(params, v_0):
    m, mu_s, mu_k, N, F_0=params
    t_span=(0, 5)
    t_eval=np.linspace(0,5,100)
    solver = solve_ivp(ode, t_span, [v_0], t_eval=t_eval, args=(params))
    
    return solver.t, solver.v[0]

plt.figure()

v_0=1e-8

for i, params in enumerate (sets):
    t,v=solve_ode(params, v_0)
    
    plt.plot(t,v)
    
plt.grid()
plt.show()

[SOLVED]

https://preview.redd.it/06fuh51g2byg1.png?width=763&format=png&auto=webp&s=65737295e579040a079883f860aa6421b781eff7

https://preview.redd.it/ujw07ajl2byg1.png?width=382&format=png&auto=webp&s=6eb87fe64f8c6838732117961effd17bd02155be

I want this to refer to a footnote so I can add a source for the triangle inequality ("triangelolikheten"), just to be on the safe side. I'm not sure if I have to since this is a course many levels above learning that theorem, but it feels safer to source it regardless. But I can't figure out how to actually get a footnote. I just get the reference to a footnote, not the footnote itself.

EDIT: I figured it out. Nevermind!!