I am having a problem with a question on variance in my stochastics class. This
ID: 3170486 • Letter: I
Question
I am having a problem with a question on variance in my stochastics class. This is how the question is worded:
"A uniformly distributed RV, x is specified within the range, 0 to 100. It is sampled 10 times at equal intervals yielding 10 discrete samples.
Find the variance of the continuous random variable x"
I calculated E[x] as 55 by using Xi values of 10, 20, 30, 40, 50, 60, 70, 80, 90, 100 and a probability of 1/10.
I then tried to calculate the variance using the continuous function: x1 to x2 [(x - m)2 × p(x)dx] = V[x] and got 202.5 using 1/10 for the probability. This seems like a very large number for the variance. Can anyone help me solve this problem? I must be using incorrect values for something.
Explanation / Answer
Result:
x
p(x)
x*p(x)
(x-mean)^2*p(x)
10
0.1
1
202.5
20
0.1
2
122.5
30
0.1
3
62.5
40
0.1
4
22.5
50
0.1
5
2.5
60
0.1
6
2.5
70
0.1
7
22.5
80
0.1
8
62.5
90
0.1
9
122.5
100
0.1
10
202.5
Total
0.900
55
825
Variance = 825
Standard deviation = 28.72281
x
p(x)
x*p(x)
(x-mean)^2*p(x)
10
0.1
1
202.5
20
0.1
2
122.5
30
0.1
3
62.5
40
0.1
4
22.5
50
0.1
5
2.5
60
0.1
6
2.5
70
0.1
7
22.5
80
0.1
8
62.5
90
0.1
9
122.5
100
0.1
10
202.5
Total
0.900
55
825
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