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(Solved): The probability density function of a continuous random variable \( X \) is \( f(x)=\alpha e^{-\bet ...
The probability density function of a continuous random variable \( X \) is \( f(x)=\alpha e^{-\beta x} \) if \( x>0 \) and \( f(x)=0 \) otherwise \( (\alpha, \beta>0) \). If the mean of \( X \) is 2, find the values of \( \alpha, \beta \) and hence find the variance of \( X \).
Expert Answer
Here the function is given by f(x)={?e??xx>00otherwise. As it is a probability density function ????f(x)dx=1 ????0f(x)dx+?0?f(x)dx=1 ????0(0)dx+?0?(?e