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The prerequisite for this course is MAC 2254 (Calculus for Engineers 2) or MAC 2312

19 / 01 / 2019 Maths

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The prerequisite for this course is MAC 2254 (Calculus for Engineers 2) or MAC 2312 (Calculus with Analytic Geometry II). The purpose of this assignment is to review some topics from these courses that will be used in STA 4821.  
A random variable X can be described by its density function fx(t) or its distribution function Fx(t). They are related as follows. 
∫ −∞
=
=
t
xx
xx
f(u)duF(t)
F(t)
dt d
f(t)  
The first two moments of a random variable X are 

∫ ∞
−∞ ∞
−∞
=⋅
=⋅
f(t)dt)tE(X
f(t)dtE(X)t
x
x
22 
The convolution g(t) is defined as 
∫ ∞ −∞ ⋅−= u)du f (tf(u)g(t) xx  
Later, these formulas will be given physical interpretations; but for now, take the viewpoint that the following exercise will get the mathematical details out of the way so that later we can concentrate on their meaning rather than their calculation.  
Fill in the following table. Show all work on separate pages. Draw the graphs of fx(t),  Fx(t) and g(t) on the graph paper provided. 



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