n 1 n For sample values X1, X2, X, the sample variance is s² = n-1 -Σ (x-x) ², where x = -- Σ x; is the sample n i=1 i=1 mean. (a) Show that the sample variance is unchanged if a constant c is added to or subtracted from each value in the sample. (b) Show that the sample variance becomes c² times its original value if each observation in the sample is multiplied by c.

Calculus For The Life Sciences
2nd Edition
ISBN:9780321964038
Author:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.
Publisher:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.
Chapter2: Exponential, Logarithmic, And Trigonometric Functions
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I need help with this parts a and b please

n
1
n
For sample values X1, X2,
X, the sample variance is s² =
n-1
-Σ (x-x) ², where x = -- Σ x; is the sample
n
i=1
i=1
mean.
(a) Show that the sample variance is unchanged if a constant c is added to or subtracted from each value in the
sample.
(b) Show that the sample variance becomes c² times its original value if each observation in the sample is multiplied
by c.
(a) If a constant c is added to or subtracted from each value in the sample, how do the sample values x, change?
Each x
becomes cx;.
remains unchanged.
becomes (x + c).
Transcribed Image Text:n 1 n For sample values X1, X2, X, the sample variance is s² = n-1 -Σ (x-x) ², where x = -- Σ x; is the sample n i=1 i=1 mean. (a) Show that the sample variance is unchanged if a constant c is added to or subtracted from each value in the sample. (b) Show that the sample variance becomes c² times its original value if each observation in the sample is multiplied by c. (a) If a constant c is added to or subtracted from each value in the sample, how do the sample values x, change? Each x becomes cx;. remains unchanged. becomes (x + c).
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