Homework Statement
Consider a Negative Binomial random variable Y ~ NB(r, p). Show (from first principles!) that E[Y] is r/p. Why does this imply Y is proper?
Homework Equations
I have no idea how to use latex, so this may be messy:
pmf of Y: [ (k+r-1)! / k!(r-1)! ] * (1-p)^r * p^k...
is divisible by 48...
so since both sides can be divisible by 48...can i conclude that f(n+2) is divisible by 48...and so conclude my whole proof altogether since I've proved both f(n) and f(n+2)
wait let me try this again
f(n+2) = (n+2)³ - 4(n+2)
= n³ + 6n² + 12n + 8 -4n - 8
since f(n) = n³-4n and proven that it was divisible by 48
f(n+2) = n³ - 4n + 6n² + 12n
= n³ - 4n + 6n(n+2)
ah thank you i think i understand it a bit more now
wait..is it f(n+2) or f(2n) ?
i thought for any even number its 2n and for odd its 2n+1
okay so
f(2) = (2)³ - 4(2) = 0 therefore for n=2 it is true
f(2n) = (2n)³ - 4(2n)
= 8n³ - 8n
= 8n(n²-1)
how do i prove from hereforth that...
Homework Statement
1. Prove that if n is an even positive integer, then n³-4n is always divisible by 48.
2. Prove taht the square of an odd integer is always of the form 8k+1, where k is an integer.
3. Observe that the last two digits of 7² are 49, the last two digits of 7³ are 43...
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