Let X1​,X2​,…,Xn​ represent a sample of observations taken from an exponentially distributed population with parameter β

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Let X1​,X2​,…,Xn​ represent a sample of observations taken from an exponentially distributed population with parameter β

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Let X1​,X2​,…,Xn​ represent a sample of observations taken from an exponentially distributed population with parameter β. Let Y=X1​+X2​+⋯+Xn​. Assuming the observations are independent random variables, identify the distribution of the random variable defined as Z=β2Y​ a) Find the distribution of Y and state any relevant defining parameters. b) Find the distribution of Z and state any relevant defining parameters.
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