Statistical Inference Question

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In summary, the conversation discusses finding a pair of numbers that satisfies certain conditions for the rounding function and the uniform distribution of a random variable. It also raises questions about the distribution of the rounding function and the difference between the rounding function and the original distribution.
  • #1
thebook
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Hi guys,

I am stuck with this problem... Please help!

Define the rounding function [.] to integers as follows:

[x] = j if x ∈ (j-0.5, j+0.5, for j = 0,+-1, +-2,...

Suppose X has a uniform distribution on the interval (a,b). i.e., X~U(a,b) a<b.

1. find a pair a and b such hat Var(X) > Var([X]) and such that VAR(X) < VAR([X])
2. Suppose that a random variable X has a continuous CDF F(x). What are the distributions of F(X) and [F(X)]? and finally R = [F(X)]-F(X)?
 
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  • #2
thebook said:
1. find a pair a and b such hat Var(X) > Var([X]) and such that VAR(X) < VAR([X])

Instead of what you wrote, I think the question should say:

1. Find a pair of numbers (a,b) such that Var(X) > Var([X]) and find another pairs of numbers (a,b) such that Var(X) < Var([X]).
 
  • #3
thebook said:
2. Suppose that a random variable X has a continuous CDF F(x). What are the distributions of F(X) and [F(X)]? and finally R = [F(X)]-F(X)?
F(X) doesn't mean anything, and neither does 'the distribution of F(x)'. F(x) is the distribution of X.
Should it read:
What are the distributions of [X] and [X]-X?
 

What is statistical inference?

Statistical inference is the process of using data from a sample to make conclusions or predictions about a larger population. It involves analyzing and interpreting data to draw meaningful insights and make decisions based on the results.

What are the types of statistical inference?

The two main types of statistical inference are estimation and hypothesis testing. Estimation involves using sample data to estimate unknown parameters of a population, while hypothesis testing involves making decisions about a population based on sample data.

What is the difference between a population and a sample?

A population is the entire group of individuals or objects that we are interested in studying, while a sample is a smaller subset of that population. Statistical inference is based on analyzing data from a sample to make conclusions about the larger population.

How do you determine the sample size for statistical inference?

The sample size needed for statistical inference depends on various factors, such as the level of confidence desired, the variability of the data, and the margin of error. Generally, a larger sample size will provide more accurate results, but it also depends on the specific analysis being performed.

What are the assumptions of statistical inference?

The main assumptions of statistical inference are that the data is representative of the population, the data is independent, and the data follows a specific probability distribution. It is important to check these assumptions before performing any statistical analysis to ensure the validity and accuracy of the results.

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