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For sample values Xx, Xx... the sample variance is s² = 1₁₁ Σ (x-x)², where x = 12 x, is the sample mean. i=1 (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.

For sample values Xx, Xx... the sample variance is s² = 1₁₁ Σ (x-x)², where x = 12 x, is the sample mean. i=1 (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 First Course in Probability (10th Edition)
A First Course in Probability (10th Edition)
10th Edition
ISBN:9780134753119
Author:Sheldon Ross
Publisher:Sheldon Ross
Chapter1: Combinatorial Analysis
Section: Chapter Questions
Problem 1.1P: a. How many different 7-place license plates are possible if the first 2 places are for letters and...
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n n For sample values X1, X2, n- ., X., the sample variance is s² = 11-1Σ (X; -x)², where x = -1 Σ x; is the sample mean. n i=1 i=1 (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 (x; +c). How does this change the sample mean X? The sample mean which simplifies to x + nc. simplifies to cx. simplifies to x + c. means the sample mean is x.
Transcribed Image Text:n n For sample values X1, X2, n- ., X., the sample variance is s² = 11-1Σ (X; -x)², where x = -1 Σ x; is the sample mean. n i=1 i=1 (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 (x; +c). How does this change the sample mean X? The sample mean which simplifies to x + nc. simplifies to cx. simplifies to x + c. means the sample mean is x.
n n For sample values x1, x2, ..., X, the sample variance is s² = - n-1 n Σ (x-x) ², where x = Σ x₁ is the sample mean. i=1 i=1 (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 (x; +c). How does this change the sample mean x? The sample mean which n becomes (CX²). i=1 remains unchanged, n becomes (x; +c). i=1
Transcribed Image Text:n n For sample values x1, x2, ..., X, the sample variance is s² = - n-1 n Σ (x-x) ², where x = Σ x₁ is the sample mean. i=1 i=1 (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 (x; +c). How does this change the sample mean x? The sample mean which n becomes (CX²). i=1 remains unchanged, n becomes (x; +c). i=1
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