The pdf of a continuous random variable X is given by $f_X(x) = egin{cases} Cx, & 0 le x le 1\ 0, & ext{otherwise.} end{cases}$ a) Find the value of C. b) Find and plot the cdf $F_X(x)$. c) Find $P(X > .5)$. d) Find the expected value of X, i.e., find $E{X}$.
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Given that the integral of the pdf from 0 to 1 is equal to 1, we have: \[ \int_{0}^{1} Cx \, dx = 1 \] \[ C \int_{0}^{1} x \, dx = 1 \] \[ C \left[ \frac{x^2}{2} \right]_{0}^{1} = 1 \] \[ C \left( \frac{1}{2} - 0 \right) = 1 \] \[ C \times \frac{1}{2} = 1 \] \[ C Show more…
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