Discrete Mathematics
Variance
The probability distribution of a random variable \(X\) is
\[\begin{array} &P(X = 1) = 0.1 &P(X = 2) = 0.2 &P( X = 3) = 0.3 &P( X = 4) = 0.4. \end{array}\]
If \( Y = 9X+14,\) what is the variance of \(Y?\)
A random variable \(X\) has \(E(X)=3\) and \(V(X)=9.\) If \[\begin{array} &Y=aX+b, &E(Y)= 6, &V(Y) = 9,\end{array}\] what are \(a(>0)\) and \(b?\)
If \( V(X) = 4 \), what is \( V(2X + 7 )? \)
If \( V(X) = 3 \) and \(E(X^2) = 10,\) what is \( (E(X))^2 ? \)
If \( V(X) = 5 \), what is \( V(2X + 4 )? \)