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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.

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.

Calculus For The Life Sciences
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
Section2.CR: Chapter 2 Review
Problem 111CR: Respiratory Rate Researchers have found that the 95 th percentile the value at which 95% of the data...
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I need help with the part attached and then part b
b) Show that the sample variance becomes c^2 times its original value if each observation in the sample is multiplied by c.

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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