How do you use a chi square table?

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To find P(X < 5.23 using the moment generating function (1-2t)^(-6), it's essential to determine the degrees of freedom, which is r=3. Access to a chi-square table is necessary, and it's important to consult the user manual to understand how the table is organized, as it may present different tails. If a chi-square table is unavailable, the probability can be expressed as a definite integral for evaluation. Understanding the table's instructions is crucial for accurate calculations. This approach will help in correctly finding the desired probability.
Artusartos
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For example, if the moment generating function is (1-2t)^(-6), then the degree of freedom r=3, right? The question is asking me to find P(X< 5.23)...I want to use the chi-square table, but I'm not sure how...


This is what the question states:

If (1-2t)^{-6}, t<1/2, is the mgf of the random variabel X, find P(X&lt; 5.23).


Thanks in advance.
 
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Artusartos said:
For example, if the moment generating function is (1-2t)^(-6), then the degree of freedom r=3, right? The question is asking me to find P(X< 5.23)...I want to use the chi-square table, but I'm not sure how...This is what the question states:

If (1-2t)^{-6}, t<1/2, is the mgf of the random variabel X, find P(X&lt; 5.23).Thanks in advance.

Do you have access to a chi-squared table? If you do, just read the user's manual! The point is that sometimes there are different ways of tabulating the same function; some tables might tabulate the left tail, others the right tail, etc. You need to read the instructions that come with the table, or at least look at the table captions.

If you do not have access to a chi-squared table, you can always express the answer in terms of a definite integral and then evaluate it is some way. There are many possibilities for this, but first you need to have the integral written down.

RGV
 
Last edited:
Ray Vickson said:
Do you have access to a chi-squared table? If you do, just read the user's manual! The point is that sometimes there are different ways of tabulating the same function; some tables might tabulate the left tail, others the right tail, etc. You need to read the instructions that come with the table, or at least look at the table captions.

If you do not have access to a chi-squared table, you can always express the answer in terms of a definite integral and then evaluate it is some way. There are many possibilities for this, but first you need to have the integral written down.

RGV

Thanks a lot...I just asked my professor about this, and I think I understand it now :)
 
Question: A clock's minute hand has length 4 and its hour hand has length 3. What is the distance between the tips at the moment when it is increasing most rapidly?(Putnam Exam Question) Answer: Making assumption that both the hands moves at constant angular velocities, the answer is ## \sqrt{7} .## But don't you think this assumption is somewhat doubtful and wrong?

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