A certain river floods every year. Suppose that the low-water mark is set at 1 and the high-water mark Y has distribution function Fy (y) = P(Y ≤ y) = 1 - y 1 1 ≤ y < 00. (a) Verify that Fy (y) is a cdf. (b) Find fy (y), the pdf of Y. (c) If the low-water mark is reset at 0 and we use a unit of measurement that is of that given previously, the high-water mark becomes Z = 10(Y-1). Find Fz(2).

A First Course in Probability (10th Edition)
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Chapter1: Combinatorial Analysis
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A certain river floods every year. Suppose that the low-water mark is set at 1 and the
high-water mark Y has distribution function
Fy (y) = P(Y ≤ y) = 1
-
y
3
1 ≤ y < 00.
(a) Verify that Fy (y) is a cdf.
(b) Find fy (y), the pdf of Y.
(c) If the low-water mark is reset at 0 and we use a unit of measurement that is of
that given previously, the high-water mark becomes Z = 10(Y-1). Find Fz(2).
Transcribed Image Text:A certain river floods every year. Suppose that the low-water mark is set at 1 and the high-water mark Y has distribution function Fy (y) = P(Y ≤ y) = 1 - y 3 1 ≤ y < 00. (a) Verify that Fy (y) is a cdf. (b) Find fy (y), the pdf of Y. (c) If the low-water mark is reset at 0 and we use a unit of measurement that is of that given previously, the high-water mark becomes Z = 10(Y-1). Find Fz(2).
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