1. Test whether the following expression is a valid CDF. The range of validity of the variable is 0 to ∞. If it is a valid CDF, obtain the corresponding pdf and its mean. If it is not a valid CDF, test whether it is a valid pdf? If it is a valid pdf, obtain the corresponding CDF and the mean. 2x 1-exp 1-exp *(x) = - [₁-x ( -5 )] + [¹-x (-43)] + [(-) P(- h(x)=1/ 1-exp 16 1

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1. Test whether the following expression is a valid CDF. The range of validity of the variable
is 0 to ∞. If it is a valid CDF, obtain the corresponding pdf and its mean. If it is not a valid
CDF, test whether it is a valid pdf? If it is a valid pdf, obtain the corresponding CDF and
the mean.
2x
x²
A(x)-[1-exp(-) ++ [¹-exp(-²3)] -+-)]
=
exp
5
16
x²
8
Transcribed Image Text:1. Test whether the following expression is a valid CDF. The range of validity of the variable is 0 to ∞. If it is a valid CDF, obtain the corresponding pdf and its mean. If it is not a valid CDF, test whether it is a valid pdf? If it is a valid pdf, obtain the corresponding CDF and the mean. 2x x² A(x)-[1-exp(-) ++ [¹-exp(-²3)] -+-)] = exp 5 16 x² 8
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