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.)
200 exam-style questions on OCR (MEI) A Level Maths 2.3 Probability, covering 2.3.1 Calculate the probability of an event, 2.3.2 Complementary events, 2.3.3 Expected frequency of an event, 2.3.4 Diagrams to calculate probabilities, 2.3.5 Mutually exclusive and independent events, 2.3.6 Add probabilities for mutually exclusive events, 2.3.7 Multiply probabilities for independent events, 2.3.8 Mutually exclusive and independent events (notation) (A-level only), 2.3.9 Venn diagrams for probabilities (A-level only), 2.3.10 Conditional probabilities (A-level only), and 2.3.11 Independence via conditional probability (A-level only). Each one has a worked solution and a mark scheme showing where the marks go.