The generating function is
Which we can expand out as
The n for which we can create n-cents using 4 and 6 cent coins are n=4, 6, 8, 10, 12, 14...
That is we can create all even numbers except 2
algebraic combinatoric 1. Let b be the number of ways to change 6 cents. Find the generating function ". For whi...
Find a generating function for the number of ways to make n cents in change using only pennies, nickels, and dimes.
1. Using generating functions, find the number of ways to make change for a $100 bill using only dollar coins and $1, $2, and $5 bills. explain in detail
What generating functions can be used to find the number of ways in which postage of r cents can be pasted on an envelope using 1-cent, 3-cent, and 20-cent stamps? (a) Assume that the order the stamps are pasted on does not matter. (b) Assume that the stamps are pasted in a row and their order matters.
Using Java programming languague find the total number of different coin changes to make change for N cents, and we have infinite supply of each of S = {5, 2, 1} valued coins.
Find the generating function to determine the number of ways to pick k objects from n objects when the ith object can appear times for and any integer . i+jn u>ι>Ι We were unable to transcribe this image
Suppose we want to make change for n cents, using the least number of coins of denominations 1, 10, and 25 cents. Consider the following greedy strategy: suppose the amount left to change is m; take the largest coin that is no more than m; subtract this coin's value from m, and repeat. Either give a counter example, to prove that this algorithm can output a non-optimal solution or prove that this algorithm always outputs an optimal solution.
3. Use the probability generating function Px)(s) to find (a) E[X(10)] (b) VarX(10)] (c) P(X(5)-2) . ( 4.2 Probability Generating Functions The probability generating function (PGF) is a useful tool for dealing with discrete random variables taking values 0,1, 2, Its particular strength is that it gives us an easy way of characterizing the distribution of X +Y when X and Y are independent In general it is difficult to find the distribution of a sum using the traditional probability...
4. Find the generating function for the number of labeled graphs where there are 1 or 2 edges at each vertex. 4. Find the generating function for the number of labeled graphs where there are 1 or 2 edges at each vertex.
7. A probability generating function encodes the probabilities of different events happening with a gener- ating function. For example, consider tossing a coin until the first time you get a heads. Then, let pn be the probability that you had to flip the coin n times until you got a heads for the first time. The probability generating function for this problem would be f(z) = Σ Pnz". 膨:1 (a) If your coin has a probability p of landing heads...
(b) What is the probability of generating a random number between 0.35 and 0.65? (c) What is the probability of generating a random number with a value less than or equal to 0.20? (d) What is the probability of generating a random number with a value greater than 0.60? (e) Generate 50 random numbers by entering =RAND() into 50 cells of an Excel worksheet. This answer has not been graded yet. (f) Compute the mean and standard deviation for the...