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, 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.

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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