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What is R N A?

Updated: 12/15/2022
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RiboNucleic Acid

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Q: What is R N A?
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Prove that nCr plus nCr minus 1 equals n plus 1Cr?

nCr + nCr-1 = n!/[r!(n-r)!] + n!/[(r-1)!(n-r+1)!] = n!/[(r-1)!(n-r)!]*{1/r + 1/n-r+1} = n!/[(r-1)!(n-r)!]*{[(n-r+1) + r]/[r*(n-r+1)]} = n!/[(r-1)!(n-r)!]*{(n+1)/r*(n-r+1)]} = (n+1)!/[r!(n+1-r)!] = n+1Cr


What is the difference between a permutation and combination?

n p =n!/(n-r)! r and n c =n!/r!(n-r)! r


Why is it said that poisson distribution is a limiting case of binomial distribution?

This browser is totally bloody useless for mathematical display but...The probability function of the binomial distribution is P(X = r) = (nCr)*p^r*(1-p)^(n-r) where nCr =n!/[r!(n-r)!]Let n -> infinity while np = L, a constant, so that p = L/nthenP(X = r) = lim as n -> infinity of n*(n-1)*...*(n-k+1)/r! * (L/n)^r * (1 - L/n)^(n-r)= lim as n -> infinity of {n^r - O[(n)^(k-1)]}/r! * (L^r/n^r) * (1 - L/n)^(n-r)= lim as n -> infinity of 1/r! * (L^r) * (1 - L/n)^(n-r) (cancelling out n^r and removing O(n)^(r-1) as being insignificantly smaller than the denominator, n^r)= lim as n -> infinity of (L^r) / r! * (1 - L/n)^(n-r)Now lim n -> infinity of (1 - L/n)^n = e^(-L)and lim n -> infinity of (1 - L/n)^r = lim (1 - 0)^r = 1lim as n -> infinity of (1 - L/n)^(n-r) = e^(-L)So P(X = r) = L^r * e^(-L)/r! which is the probability function of the Poisson distribution with parameter L.


How many groups of 20 can you choose out of 23?

Combinations of r from n without replacement is c(n,r) = n!/(n-r)!r! c(n,r) = 23!/20!3! c(n,r) = 1771.


General formulae for the combination nCr in terms of n and r?

nCr=n!/(r!(n-r)!)


What is ncr value?

n(n-r)/r


An algorithm that generates all r-permutations of an n-element set?

P(n,r)=(n!)/(r!(n-r)!)This would give you the number of possible permutations.n factorial over r factorial times n minus r factorial


How do you evaluate combinations?

If you have n objects and you are choosing r of them, then there are nCr combinations. This is equal to n!/( r! * (n-r)! ).


How do you find the coefficients of the terms in the binomial expansion?

The coefficient of x^r in the binomial expansion of (ax + b)^n isnCr * a^r * b^(n-r)where nCr = n!/[r!*(n-r)!]


How do you do combinations in math?

nCr=n!/r!/(n-r)!


What is 6C2?

nCr = (n!)/(r!(n-r)!) and the answer is 15


How do you expand binomials A plus b to the degree of n?

It isnC0*A^n*b^0 + nC1*A^(n-1)*b^1 + ... + nCr*A^(n-r)*b^r + ... + nCn*A^0*b^n where nCr = n!/[r!*(n-r)!]