The entropy function occurs naturally in estimates of sums of binomial coefficients. Show that the estimate E (n) 211(a)•n 01 = + (1 — a)r = () ak • (1 — ark E ()(1 _ k=0 0( a k — a)

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The entropy function occurs naturally in estimates of sums of binomial coefficients. Show that the estimate
E (n) 211(a)•n 01 = + (1 — a)r = () ak • (1 — ark E ()(1 _ k=0 0(
a k — a)

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Answered Same DayDec 22, 2021

Answer To: The entropy function occurs naturally in estimates of sums of binomial coefficients. Show that the...

Robert answered on Dec 22 2021

123 Votes

Sol:
We know by binomial theorem that,
( ( ))
∑(

) ( )
∑ (

) ( )
∑ (

) ( ) (

)
Using the result above, we get,
∑ (

) ( ) (

)
⟹ 2? <
⟹ ? < ?
⟹ (
?
?
) <
⟹ log (
?
?
) < 0
⟹ ? log...

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The entropy function occurs naturally in estimates of sums of binomial coefficients. Show that the estimate E (n) 211(a)•n 01 = + (1 — a)r = () ak • (1 — ark E ()(1 _ k=0 0( a k — a)

Answer To: The entropy function occurs naturally in estimates of sums of binomial coefficients. Show that the...

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