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-(Continwous Random Variable) (25 pts) (a) (Spts) The or False. No need to justify Let \( X \) be a continuous randotn wariable with CDF \( F(x) \) and \( \mathrm{PDF} f_{x}(x) \). (i) (Spts) \( P[11 \end{array}\right. \] Find \( E[Y] \) (c) \( (5 p t s) \) Fandom variables \( x \) has pdf given by \[ f(x)=\left\{\begin{array}{cc} a c-1 & x>0 \\ 0 & \text { else } \end{array}\right. \] Find \( c \) (d) (ipto) Let a random variable \( N \) have the following PDF: \[ f(x)=\frac{1}{\sqrt{2} \pi^{2}} e^{-i+y^{2}},-\infty