Let Z n , n ≥ 1 , be a sequence of random variables and ca constant such that for each ε > 0 , P { | Z n − c | > ε } → 0 as n → ∞ . Show that for any bounded continuous function g, E [ g ( Z n ) ] → g ( c ) as n → ∞
Let Z n , n ≥ 1 , be a sequence of random variables and ca constant such that for each ε > 0 , P { | Z n − c | > ε } → 0 as n → ∞ . Show that for any bounded continuous function g, E [ g ( Z n ) ] → g ( c ) as n → ∞
Solution Summary: The author explains that for any bounded continuous function g, Eleft (Z_n-c) and epsilon (n).
Let
Z
n
,
n
≥
1
, be a sequence of random variables and ca constant such that for each
ε
>
0
,
P
{
|
Z
n
−
c
|
>
ε
}
→
0
as
n
→
∞
. Show that for any bounded continuous function g,
E
[
g
(
Z
n
)
]
→
g
(
c
)
as
n
→
∞
Expression, rule, or law that gives the relationship between an independent variable and dependent variable. Some important types of functions are injective function, surjective function, polynomial function, and inverse function.
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