Determining the chi-square distribution
If X1 and X2 are independent random variables, X1 has a chi-square distribution with 3 degrees of freedom, and X1 + X2 has a chi-square distribution with 7 degrees of freedom. Prove that X2 has a chi-square distribution with 4 degrees of freedom.
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The solubility of compound A in ethanol is 0.4g per 100ml at 0degrees celsius and 5.0g per 100 ml at 75 degreescelsius. What is the minimum amount of solvent needed torecrystallize an 8.0g sample of compound A?
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If X1 and X2 are independent random variables, X1 has a chi-square distribution with 3 degrees of freedom, and X1 + X2 has a chi-square distribution with 7 degrees of freedom. Prove that X2 has a chi-square distribution
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