Let A be a fixed positive constant, and define the function f(x) by f(x) - e-if x>0 and f(x) = de^ if x < 0. (a) Verify that f(x) is a pdf. (b) If X is a random variable with pdf given by f(x), find P(X

Calculus For The Life Sciences
2nd Edition
ISBN:9780321964038
Author:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.
Publisher:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.
Chapter14: Discrete Dynamical Systems
Section14.3: Determining Stability
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A.z.
Let A be a fixed positive constant, and define the function f(x) by f(r) de if
x>0 and f(x) = Ae^¹ if x < 0.
-
(a) Verify that f(x) is a pdf.
(b) If X is a random variable with pdf given by f(x), find P(X <t) for all t. Evaluate
all integrals.
(c) Find P(|X<t) for all t. Evaluate all integrals.
Transcribed Image Text:A.z. Let A be a fixed positive constant, and define the function f(x) by f(r) de if x>0 and f(x) = Ae^¹ if x < 0. - (a) Verify that f(x) is a pdf. (b) If X is a random variable with pdf given by f(x), find P(X <t) for all t. Evaluate all integrals. (c) Find P(|X<t) for all t. Evaluate all integrals.
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