Question

3. Consider the function \[ f(x)=\left\{\begin{array}{ll} C\left(2 x-x^{3}\right) & 0<x<\frac{5}{2} \\ 0 & \text { otherwise } \end{array}\right. \] Could $ f $ be a probability density function ? If so, determine $ C $. Repeat if $ f(x) $ were given by \[ f(x)=\left\{\begin{array}{ll} C^{\prime}\left(2 x-x^{2}\right) & 0<x<\frac{5}{2} \\ 0 & \text { otherwise } \end{array}\right. \]

          3. Consider the function
\[
f(x)=\left\{\begin{array}{ll}
C\left(2 x-x^{3}\right) & 0<x<\frac{5}{2} \\
0 & \text { otherwise }
\end{array}\right.
\]

Could \( f \) be a probability density function ? If so, determine \( C \). Repeat if \( f(x) \) were given by
\[
f(x)=\left\{\begin{array}{ll}
C^{\prime}\left(2 x-x^{2}\right) & 0<x<\frac{5}{2} \\
0 & \text { otherwise }
\end{array}\right.
\]

$3. Consider the function f(x)={ C(2 x-x^3) 0<x<(5)/(2) 0 otherwise . Could f be a probability density function ? If so, determine C. Repeat if f(x) were given by f(x)={ C^'(2 x-x^2) 0<x<(5)/(2) 0 otherwise .$

Added by Patricia M.

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