Let x 1 , x 2 , ⋯ , x n be independent random variables, each with density function f ( x ) , expected value μ , and variance σ 2 . Define the sample mean by x ¯ = ∑ i = 1 n x i . Show that E ( x ¯ ) = μ , and Var ( x ¯ ) = σ 2 / n . (See Problems 5.9 , 5.13 , and 6.15. .
Let x 1 , x 2 , ⋯ , x n be independent random variables, each with density function f ( x ) , expected value μ , and variance σ 2 . Define the sample mean by x ¯ = ∑ i = 1 n x i . Show that E ( x ¯ ) = μ , and Var ( x ¯ ) = σ 2 / n . (See Problems 5.9 , 5.13 , and 6.15. .
Let
x
1
,
x
2
,
⋯
,
x
n
be independent random variables, each with density function
f
(
x
)
, expected value
μ
,
and variance
σ
2
.
Define the sample mean by
x
¯
=
∑
i
=
1
n
x
i
.
Show that
E
(
x
¯
)
=
μ
,
and
Var
(
x
¯
)
=
σ
2
/
n
.
(See Problems
5.9
,
5.13
,
and
6.15.
.
Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, subject and related others by exploring similar questions and additional content below.
Continuous Probability Distributions - Basic Introduction; Author: The Organic Chemistry Tutor;https://www.youtube.com/watch?v=QxqxdQ_g2uw;License: Standard YouTube License, CC-BY
Probability Density Function (p.d.f.) Finding k (Part 1) | ExamSolutions; Author: ExamSolutions;https://www.youtube.com/watch?v=RsuS2ehsTDM;License: Standard YouTube License, CC-BY
Find the value of k so that the Function is a Probability Density Function; Author: The Math Sorcerer;https://www.youtube.com/watch?v=QqoCZWrVnbA;License: Standard Youtube License