A random variable X has density function f(x)=(1/2)e^(-abs(x)). Prove that the moment-generating function of X is Mx(t)=1/(1-t^2)

1 answer below »
A random variable X has density function f(x)=(1/2)e^(-abs(x)). Prove that the moment-generating function of X is Mx(t)=1/(1-t^2)

Answered Same DayDec 20, 2021

Answer To: A random variable X has density function f(x)=(1/2)e^(-abs(x)). Prove that the moment-generating...

Robert answered on Dec 20 2021
116 Votes
F(x)=1/2e^(-abs(x))
F(x) can be rewritten as
F(x)=(1/2)e^(-x) from x=0 to x=∞ (i.e.) for positiv
e numbers
F(x)=(1/2)e^(x) from x=-∞ to x=0 (i.e.) for negative numbers
F(x)=not defined at x=0
M(x)=∫ ( ) ( )
M(x)=∫ ( ) ( ) ( )


+∫ ( ) ( ) ( )



=∫...
SOLUTION.PDF

Answer To This Question Is Available To Download

Related Questions & Answers

More Questions »

Submit New Assignment

Copy and Paste Your Assignment Here
April
January
February
March
April
May
June
July
August
September
October
November
December
2025
2025
2026
2027
SunMonTueWedThuFriSat
30
31
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
1
2
3
00:00
00:30
01:00
01:30
02:00
02:30
03:00
03:30
04:00
04:30
05:00
05:30
06:00
06:30
07:00
07:30
08:00
08:30
09:00
09:30
10:00
10:30
11:00
11:30
12:00
12:30
13:00
13:30
14:00
14:30
15:00
15:30
16:00
16:30
17:00
17:30
18:00
18:30
19:00
19:30
20:00
20:30
21:00
21:30
22:00
22:30
23:00
23:30