Foram encontradas 70 questões.
Para estimar, por máxima verossimilhança (MV) ou pelo método dos momentos (MM), o único parâmetro de dada distribuição de probabilidades, seleciona-se uma amostra de tamanho n.
A função densidade da distribuição é:
fx(x) = θxθ-1 , para 0 < x < 1 e zero caso contrário.Além disso, considere:
Então, os estimadores de MV e de MM (com base na média da distribuição) para θ são, respectivamente:
Provas
Seja X uma variável aleatória contínua e Y= G(X) uma função de X tal que, no domínio da fx(x), densidade da X, as derivadas de 1ª e de 2ª ordem da G(X) são estritamente negativas. Considerando,
fy(y)= função densidade de probabilidade de Y;
fx-1(x) = função inversa da densidade de X;
= derivada de f(x) com respeito à x;
E(X) = esperança matemática de X;
h[f(X)] = função composta de f com h.
Então é correto afirmar que:
Provas
A capacidade de um time de futebol de marcar gols em uma única partida é uma variável aleatória. A tabela a seguir apresenta a probabilidade de certo time marcar um número mínimo (Y) de gols em uma partida:
Isso significa que o número médio de gols marcados por esse time em uma única partida de futebol é igual a:
Provas
Com a finalidade de estimar a proporção p de indivíduos de certa
população, com determinado atributo, através da proporção
amostral 
é extraída uma amostra de tamanho n, grande,
compatível com um erro amostral de ε e com um grau de
confiança de (1-α). Assim, é correto afirmar que:
Provas
Provas
Considere a variável aleatória bidimensional (X,Y) cuja função de densidade conjunta é dada por:
fx,y(x,y) = 3/4. y.x2,0 < x < 2 e 0 < y < 1 e zero caso contrário. Então:
Provas
- FundamentosAmostra
- Amostragem
- Estatística DescritivaMedidas de Dispersão
- Estatística DescritivaMedidas de Tendência Central
Considere os estimadores a seguir, tendo em vista a média populacional μ , a partir de uma amostra de tamanho n.
Se a variância populacional é finita, sobre as propriedades de 
e 
correto afirmar que:
Provas
Suponha que uma amostra de tamanho n = 5 é extraída de uma população Normal, com média desconhecida, obtendo as seguintes observações:
X1 = 3, X2 = 5, X3 = 6, X4 = 9 e X5 = 12
São dados ainda os seguintes valores, retirados da tabela da distribuição Qui-Quadrado:
Se a população tem variância verdadeira σ2 = 4 em nova amostra (n=5), a probabilidade de se observar uma variância amostral maior do que a anterior é de:
Provas
TEXT II
The backlash against big data
[…]
Big data refers to the idea that society can do things with a large body of data that weren’t possible when working with smaller amounts. The term was originally applied a decade ago to massive datasets from astrophysics, genomics and internet search engines, and to machine-learning systems (for voice-recognition and translation, for example) that work well only when given lots of data to chew on. Now it refers to the application of data-analysis and statistics in new areas, from retailing to human resources. The backlash began in mid-March, prompted by an article in Science by David Lazer and others at Harvard and Northeastern University. It showed that a big-data poster-child—Google Flu Trends, a 2009 project which identified flu outbreaks from search queries alone—had overestimated the number of cases for four years running, compared with reported data from the Centres for Disease Control (CDC). This led to a wider attack on the idea of big data.
The criticisms fall into three areas that are not intrinsic to big data per se, but endemic to data analysis, and have some merit. First, there are biases inherent to data that must not be ignored. That is undeniably the case. Second, some proponents of big data have claimed that theory (ie, generalisable models about how the world works) is obsolete. In fact, subject-area knowledge remains necessary even when dealing with large data sets. Third, the risk of spurious correlations—associations that are statistically robust but happen only by chance—increases with more data. Although there are new statistical techniques to identify and banish spurious correlations, such as running many tests against subsets of the data, this will always be a problem.
There is some merit to the naysayers' case, in other words. But these criticisms do not mean that big-data analysis has no merit whatsoever. Even the Harvard researchers who decried big data "hubris" admitted in Science that melding Google Flu Trends analysis with CDC’s data improved the overall forecast—showing that big data can in fact be a useful tool. And research published in PLOS Computational Biology on April 17th shows it is possible to estimate the prevalence of the flu based on visits to Wikipedia articles related to the illness. Behind the big data backlash is the classic hype cycle, in which a technology’s early proponents make overly grandiose claims, people sling arrows when those promises fall flat, but the technology eventually transforms the world, though not necessarily in ways the pundits expected. It happened with the web, and television, radio, motion pictures and the telegraph before it. Now it is simply big data’s turn to face the grumblers.
(From http://www.economist.com/blogs/economist explains/201 4/04/economist-explains-10)
Provas
TEXT I
Will computers ever truly understand what we’re saying?
Date: January 11, 2016
Source University of California - Berkeley
Summary:
If you think computers are quickly approaching true human communication, think again. Computers like Siri often get confused because they judge meaning by looking at a word’s statistical regularity. This is unlike humans, for whom context is more important than the word or signal, according to a researcher who invented a communication game allowing only nonverbal cues, and used it to pinpoint regions of the brain where mutual understanding takes place.
From Apple’s Siri to Honda’s robot Asimo, machines seem to be getting better and better at communicating with humans. But some neuroscientists caution that today’s computers will never truly understand what we’re saying because they do not take into account the context of a conversation the way people do.
Specifically, say University of California, Berkeley, postdoctoral fellow Arjen Stolk and his Dutch colleagues, machines don’t develop a shared understanding of the people, place and situation - often including a long social history - that is key to human communication. Without such common ground, a computer cannot help but be confused.
“People tend to think of communication as an exchange of linguistic signs or gestures, forgetting that much of communication is about the social context, about who you are communicating with,” Stolk said.
The word “bank,” for example, would be interpreted one way if you’re holding a credit card but a different way if you’re holding a fishing pole. Without context, making a “V” with two fingers could mean victory, the number two, or “these are the two fingers I broke.”
“All these subtleties are quite crucial to understanding one another,” Stolk said, perhaps more so than the words and signals that computers and many neuroscientists focus on as the key to communication. “In fact, we can understand one another without language, without words and signs that already have a shared meaning.”
(Adapted from http://www.sciencedaily.com/releases/2016/01/1 60111135231.htm)
Based on the summary provided for Text I, mark the statements below as TRUE (T) or FALSE (F).
( ) Contextual clues are still not accounted for by computers.
( ) Computers are unreliable because they focus on language patterns.
( ) A game has been invented based on the words people use.
The statements are, respectively:
Provas
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