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For sample values X1, X2. X the sample variance is s² = (x-x)², where x = x, is the sample 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 (x+c). How does this change the sample mean X? The sample mean which becomes n (cx;). remains unchanged, becomes (x,+c). n i=1

For sample values X1, X2. X the sample variance is s² = (x-x)², where x = x, is the sample 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 (x+c). How does this change the sample mean X? The sample mean which becomes n (cx;). remains unchanged, becomes (x,+c). n i=1

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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I need help with parts a and b

n n For sample values X1, X2, X, the sample variance is s² = n-1 -Σ (x-x)², where x = -Σx; 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 (x; +c). How does this change the sample mean X? The sample mean which n Σ(α). becomes (cx). n i=1 remains unchanged, n becomes n Σ (x+c). i=1
Transcribed Image Text:n n For sample values X1, X2, X, the sample variance is s² = n-1 -Σ (x-x)², where x = -Σx; 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 (x; +c). How does this change the sample mean X? The sample mean which n Σ(α). becomes (cx). n i=1 remains unchanged, n becomes n Σ (x+c). i=1
n For sample values X1, X2, X, the sample variance is s² = 1 n n-1 -Σ (x-x)², v where x = x; is the sample - i=1 n 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 (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 For sample values X1, X2, X, the sample variance is s² = 1 n n-1 -Σ (x-x)², v where x = x; is the sample - i=1 n 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 (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.
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