Problem 2) For the following random variable X. x<-3 0 0.4 Fx(x)= 0.8 [1 EXIDI -3≤x<5 5≤x<7 x27 a) Find the variance of the X. b) Find PX/B(x), where the condition B = {X>0}. c) Find E[XB]. DY

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**Problem 2)** For the following random variable \(X\).

\[ 
F_X(x) =
  \begin{cases} 
   0 & x < -3 \\
   0.4 & -3 \le x < 5 \\
   0.8 & 5 \le x < 7 \\
   1 & x \ge 7 
  \end{cases}
\]

a) Find the variance of \(X\).

b) Find \(P_{X|B}(x)\), where the condition \(B = \{X > 0\}\).

c) Find \(E[X|B]\).

d) Find \(\text{Var}[X|B]\).
Transcribed Image Text:**Problem 2)** For the following random variable \(X\). \[ F_X(x) = \begin{cases} 0 & x < -3 \\ 0.4 & -3 \le x < 5 \\ 0.8 & 5 \le x < 7 \\ 1 & x \ge 7 \end{cases} \] a) Find the variance of \(X\). b) Find \(P_{X|B}(x)\), where the condition \(B = \{X > 0\}\). c) Find \(E[X|B]\). d) Find \(\text{Var}[X|B]\).
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