1) Find the first four moments about the value 8 for the set of observations: 5,7,8,8,10,11 2)Find the first - Maths - Vector Algebra

Question

1) Find the first four moments about the value 8 for the set of
observations: 5,7,8,8,10,11
2)Find the first four moments about zero for the set of
observations : -3,-2,1,3,4
3) Find the first four moments about mean for the set of
observations: 16,19,22,23,25
4) The first four raw moments of a distribution are 0 9,1 7,3 1 and
8 2 respectively Find the first four central moments of the
distribution

Shivam Mishra · Accepted Answer

Dear Student,
Please find below the solution to the asked query:

2
 We have:-3,-2,1,3,4We want first four moments about 0

x
x-0=x
(x-0)2=x2
(x-0)3=x3
(x-0)4=x4

-3
-3
9
-27
81

-2
-2
4
-8
16

1
1
1
1
1

3
3
9
27
81

4
4
16
64
256

Total
3
39
57
435

Let m1,m2,m3 and m4 be first four momentsm1=∑xn=35m2=∑x2n=395m3=∑x3n=575m4=∑x45=4355=733
 We have 16,19,22,23,25Meanx¯=16+19+22+23+255=1055=21

x
x-xÌ„
(x-xÌ„)2
(x-xÌ„)3
(x-xÌ„)4

16
-5
25
-125
625

19
-2
4
-8
16

22
1
1
1
1

23
2
4
8
16

25
4
16
64
256

Total
0
50
-60
914

Let m1,m2,m3 and m4 be first four momentsm1=∑x-x¯n=05=0m2=∑x-x¯2n=505=10m3=∑x-x¯3n=-605=-12m4=∑x-x¯45=9145=182
8Please post your other queries in different thread and only one query in one thread
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x	x-0=x	(x-0)²=x²	(x-0)³=x³	(x-0)⁴=x⁴
-3	-3	9	-27	81
-2	-2	4	-8	16
1	1	1	1	1
3	3	9	27	81
4	4	16	64	256
Total	3	39	57	435

x	x-x̄	(x-x̄)²	(x-x̄)³	(x-x̄)⁴
16	-5	25	-125	625
19	-2	4	-8	16
22	1	1	1	1
23	2	4	8	16
25	4	16	64	256
Total	0	50	-60	914