MATH2560H Target Concept 01 Cumulative Distribution Functions
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Target Concept 01
Cumulative Distribution Functions
1 Finding CDFs
1. 1 Problem 1. 1
Given f(y) = cy2 , 0 ≤ y ≤ 2 and 0 elsewhere, find the value of c for which f(y) is a valid density function, then find the explicit form of FY (y). Use this last to determine P[Y > 1].
1.2 Problem 1.2
After extensive atmospheric sampling and data analysis, an environmental scientist decides that the distribution of measurements of the sulfur dioxide concentration X (in parts per million) in the air near a certain oil refinery can be closely approximated by the density function:
(a) Find FX (x), the cumulative distribution function (CDF) of X.
(b) Find the numerical value of E[X].
(c) Find the numerical value of
Specifications for Success
To obtain satisfactory on this assignment, all of the criteria below must be met
• All problems are attempted.
• Concluding statements are present where appropriate.
• Logic in derivations correct.
• Cumulative distribution function derivations are correct.
• Probability calculations are correct.
2023-02-22