Docsity
Docsity
Prepare for your exams
Prepare for your exams

Study with the several resources on Docsity

Earn points to download
Earn points to download

Earn points by helping other students or get them with a premium plan

Guidelines and tips
Guidelines and tips
Sell on Docsity
Sell on Docsity
Docsity AI
Docsity AI
Log inSign up

Prepare for your exams

Study with the several resources on Docsity

Find documents

Prepare for your exams with the study notes shared by other students like you on Docsity

Search for your university

Find the specific documents for your university's exams

Docsity AINEW

Summarize your documents, ask them questions, convert them into quizzes and concept maps

Explore questions

Clear up your doubts by reading the answers to questions asked by your fellow students

Earn points to download

Earn points by helping other students or get them with a premium plan

Share documents
download point icon20 Points

For each uploaded document

Answer questions
download point icon5 Points

For each given answer (max 1 per day)

All the ways to get free points
Get points immediately

Choose a premium plan with all the points you need

Study Opportunities

Choose your next study program

Get in touch with the best universities in the world. Search through thousands of universities and official partners

Community

Ask the community

Ask the community for help and clear up your study doubts

Free resources

Our save-the-student-ebooks!

Download our free guides on studying techniques, anxiety management strategies, and thesis advice from Docsity tutors

Probability Distribution and Statistics Calculation in Simple Random Sampling, Exercises of Calculus for Engineers

Academy CollegeCalculus for Engineers

This document shows the calculation of probability distribution and statistics for a simple random sampling with replacement from a population of students' ages in a statistics group at unam. The frequencies, probabilities, and moments of the distribution, as well as the formula for the likelihood function and the probability distribution of the sample mean. The data consists of the ages of students in the group and their respective frequencies.

Typology: Exercises

2019/2020

Uploaded on 12/11/2021

fabricio-ortega-ramirez
fabricio-ortega-ramirez 🇺🇸

2 documents

1 / 4

Toggle sidebar

This page cannot be seen from the preview

Don't miss anything!

bg1
Muestreo aleatorio simple con reemplazo
Posibles muestras de tamaño n=2
X=edad N(X) X1 X2 P(X1)=N(X1)/N P(X2)=N(X2)/N
19 10 19 19 0.32258065 0.32258065
20 15 19 20 0.32258065 0.48387097
21 4 19 21 0.32258065 0.12903226
22 1 19 22 0.32258065 0.03225806
23 1 19 23 0.32258065 0.03225806
20 19 0.48387097 0.32258065
Suma: N= 31 20 20 0.48387097 0.48387097
20 21 0.48387097 0.12903226
20 22 0.48387097 0.03225806
20 23 0.48387097 0.03225806
21 19 0.12903226 0.32258065
21 20 0.12903226 0.48387097
X f(x) 21 21 0.12903226 0.12903226
19 0.32258065 21 22 0.12903226 0.03225806
20 0.48387097 21 23 0.12903226 0.03225806
21 0.12903226 22 19 0.03225806 0.32258065
22 0.03225806 22 20 0.03225806 0.48387097
23 0.03225806 22 21 0.03225806 0.12903226
22 22 0.03225806 0.03225806
Suma: 1 22 23 0.03225806 0.03225806
23 19 0.03225806 0.32258065
Media poblacional: 23 20 0.03225806 0.48387097
m= 19.9677419 23 21 0.03225806 0.12903226
23 22 0.03225806 0.03225806
Varianza poblacional: 23 23 0.03225806 0.03225806
0.86992716
X=Edad de los estudiantes del
grupo 7 de estadística de la FI
UNAM en el semestre 2020-2
Número de estudiantes
por edad:
Distribución de la
Población:
s2=
pf3
pf4

Partial preview of the text

Download Probability Distribution and Statistics Calculation in Simple Random Sampling and more Exercises Calculus for Engineers in PDF only on Docsity!

Muestreo aleatorio simple con reemplazo

X=Edad de los estudiantes del Número de estudiantes por edad: Distribución de la Población:

 - Posibles muestras de tamaño n= - 19 10 19 19 0.32258065 0. X=edad N(X) X1 X2 P(X1)=N(X1)/N P(X2)=N(X2)/N - 20 15 19 20 0.32258065 0. - 21 4 19 21 0.32258065 0. - 22 1 19 22 0.32258065 0. - 23 1 19 23 0.32258065 0. - 20 19 0.48387097 0.
  • Suma: N= 31 20 20 0.48387097 0. - 20 21 0.48387097 0. - 20 22 0.48387097 0. - 20 23 0.48387097 0. - 21 19 0.12903226 0. - 21 20 0.12903226 0. - X f(x) 21 21 0.12903226 0. - 19 0.32258065 21 22 0.12903226 0. - 20 0.48387097 21 23 0.12903226 0. - 21 0.12903226 22 19 0.03225806 0. - 22 0.03225806 22 20 0.03225806 0. - 23 0.03225806 22 21 0.03225806 0. - 22 22 0.03225806 0.
  • Suma: 1 22 23 0.03225806 0. - 23 19 0.03225806 0.
  • Media poblacional: 23 20 0.03225806 0. - m= 19.9677419 23 21 0.03225806 0. - 23 22 0.03225806 0.
  • Varianza poblacional: 23 23 0.03225806 0. - 0.
    • UNAM en el semestre 2020- grupo 7 de estadística de la FI

n= 2

Media muestral P(X1,X2)=P(X1)*P(X2) -- Xmt P(Xmt) Xmt f(Xmt) 0.104058272632674 19 0.10405827 19 0. 0.156087408949011 19.5 0.15608741 19.5 0. 0.04162330905307 20 0.04162331 20 0. 0.010405827263268 20.5 0.01040583 20.5 0. 0.010405827263268 21 0.01040583 21 0. 0.156087408949011 19.5 0.15608741 21.5 0. 0.234131113423517 20 0.23413111 22 0. 0.062434963579605 20.5 0.06243496 22.5 0. 0.015608740894901 21 0.01560874 23 0. 0.015608740894901 21.5 0. 0.04162330905307 20 0.04162331 Suma: 1. 0.062434963579605 20.5 0. 0.016649323621228 21 0.01664932 Media muestral: 0.004162330905307 21.5 0.00416233 E{Xmt}= 19. 0.004162330905307 22 0. 0.010405827263268 20.5 0. 0.015608740894901 21 0. 0.004162330905307 21.5 0. 0.001040582726327 22 0.00104058 V{Xmt}= 0. 0.001040582726327 22.5 0. 0.010405827263268 21 0. 0.015608740894901 21.5 0. 0.004162330905307 22 0. 0.001040582726327 22.5 0. 0.001040582726327 23 0. 1 1 Función de verosimilitud de la muestra Probabilidad para esa media muestral: Distribución de muestreo de la media muestral: Varianza de la distribución muestral de la media: 1 0

Probabilidad

¿Cuál es la probabilidad de que al tomar una muestra de tamaño 2, la media de la muestra sea menor que 20 años? ¿Cuál es la probabilidad de que al tomar una muestra de tamaño 2, la media de la muestra sea de entre 20 y 22 años? ¿Cuál es la probabilidad de que la media de la muestra sea al menos 20 años?