[Steps Shown] The double exponential random variable with mean zero and variance σ ^2 has a density f(x)=(1)/(2beta)e^-(|x|)/(beta) where σ
Question: The double exponential random variable with mean zero and variance \({{\sigma }^{2}}\) has a density
\[f\left( x \right)=\frac{1}{2\beta }{{e}^{-\frac{|x|}{\beta }}}\]where \({{\sigma }^{2}}=2{{\beta }^{2}}\)
- Find the method of moments estimate of \(\beta \)
- Find the maximum likelihood estimate of \(\beta \)
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