Example 7-18. Show that eitx =1+ (eit - 1) x(1) + (eit – 1)². T+.. x(2) + (eit – 1)* . r! where xr) = x (x- 1) (x- 2)... (x-r+ 1). Hence show that Ho = [D" ¢(t)]; = 0, where D = d( eit) and H is the rth factorial moment.

MATLAB: An Introduction with Applications
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Example 7-18. Show that
eitx =1+ (eit – 1) x(1) + (eit – 1)². T+..
x(2)
2!
+ (eit – 1)r.
r!
+
where x(r) = x (x- 1) (x – 2) ...
(x - r + 1). Hence show that
d
Ho' = [D ¢(t)]t = 0, where D =7c eith and H is the rth factorial moment.
Transcribed Image Text:Example 7-18. Show that eitx =1+ (eit – 1) x(1) + (eit – 1)². T+.. x(2) 2! + (eit – 1)r. r! + where x(r) = x (x- 1) (x – 2) ... (x - r + 1). Hence show that d Ho' = [D ¢(t)]t = 0, where D =7c eith and H is the rth factorial moment.
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