Show method selection, derivation, conditions, units, verification, and interpretation.
U07 · L06
Name
Date
1
State the central method of Expected Value, Variance & Risk Interpretation and list the conditions that must be checked.
Faculty solution: Use integrating outcomes weighted by probability density. State the relevant hypotheses, domain or interval, units when applicable, and a verification plan.
2
For f(x)=2x on [0,1], find E[X].
Faculty solution: ∫₀¹2x²dx=2/3.
3
Find E[X²].
Faculty solution: ∫₀¹2x³dx=1/2.
4
A learner makes an error by dropping density, pressure, probability, or physical units. Explain the first invalid step and repair the reasoning.
Faculty solution: The first invalid step is dropping density, pressure, probability, or physical units. Return to the governing definition or theorem, restore the missing condition, and verify the corrected result.
5
Create a short application of Expected Value, Variance & Risk Interpretation in mechanical work, fluids, structures, reliability, and probabilistic decision-making. Define variables and identify the quantity an integral, differential equation, sequence, or series would measure.
Faculty solution: A defensible response defines variables and units, states assumptions, builds the correct mathematical object, and interprets its value in mechanical work, fluids, structures, reliability, and probabilistic decision-making.
6
Describe two independent ways to verify a result from Expected Value, Variance & Risk Interpretation.
Faculty solution: Use an exact structural check such as differentiation, substitution, partial sums, or theorem hypotheses; then compare with numerical, graphical, dimensional, or limiting evidence.