The continuous random variable WWW represents the daily electrical energy produced by a specific solar array (in kWh) and has probability density function g(w)g(w)g(w) given by
g(w)={124w0≤w≤4164<w≤80otherwise g(w) = \begin{cases} \frac{1}{24}w & 0 \le w \le 4 \\ \frac{1}{6} & 4 < w \le 8 \\ 0 & \text{otherwise} \end{cases} g(w)=⎩⎨⎧241w6100≤w≤44<w≤8otherwiseSketch the graph of g(w)g(w)g(w).
Determine the conditional probability P(2≤W≤6∣W≤7)P(2 \le W \le 6 \mid W \le 7)P(2≤W≤6∣W≤7).
A secondary random variable VVV, representing daily ambient temperature in degrees Celsius, is such that E(V)=9E(V) = 9E(V)=9 and Var(V)=0.75Var(V) = 0.75Var(V)=0.75.
Calculate E(5V2−18W+7)E(5V^2 - 18W + 7)E(5V2−18W+7).
Show your working clearly. (Solutions relying on calculator technology are not acceptable.)
