Hi all,
I have found the mean and standard deviation of the length of a part using the probability density function I was given.
Density function of individual part is:
f_X (x)={ 10, 20.25<x<20.35
0, otherwise
Mean = 20.30 mm
Standard Deviation = 0.1/(sqrt12) mm
5 of these parts are then randomly chosen and put end-to-end to create a new combined part with length, W.
I need to find the mean and standard deviation of this new part??
I can only seem to find formulas for combining means and deviations of sample sizes, not for combining parts with the same mean and deviation.
Any help would be greatly appreciated.
I mean the pooling formulas for mean and standard deviation all use sample size n for each group. For instance:
To find the mean for two groups combined you use μ = (n1μ1 + n2μ2) / n, where n is the sample size of the groups. To find the standard deviation you would use SD = [ s₁(n₁ - 1) + s₂(n₂ - 1) ] / ( n₁ + n₂ - 2). However, I don't have a sample size for the individual parts so I'm not sure where to go from here.
Ah ok - so you found equations for pooling based on sample estimates.
http://en.wikipedia.org/wiki/Expected_value#Linearity
http://en.wikipedia.org/wiki/Standar...cal_properties
Since you're looking for the expectation and standard deviation of the sum of two independent random variables those links should help.
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