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Coupon collector's problem. In probability theory, the coupon collector's problem refers to mathematical analysis of "collect all coupons and win" contests. It asks the following question: if each box of a given product (e.g., breakfast cereals) contains a coupon, and there are n different types of coupons, what is the probability that more ...
The accrued interest is based on the day count convention, coupon rate, and number of days from the preceding coupon payment date. [2] The clean price more closely reflects changes in value due to issuer risk and changes in the structure of interest rates. Its graph is smoother than that of the dirty price.
However, from December 1982 through December 2011, the all-items CPI-E rose at an annual average rate of 3.1 percent, compared with increases of 2.9 percent for both the CPI-U and CPI-W. [28] This suggests that the elderly have been losing purchasing power at the rate of roughly 0.2 (=3.1–2.9) percentage points per year.
Consider a bond with a $1000 face value, 5% coupon rate and 6.5% annual yield, with maturity in 5 years. [26] The steps to compute duration are the following: 1. Estimate the bond value The coupons will be $50 in years 1, 2, 3 and 4. Then, on year 5, the bond will pay coupon and principal, for a total of $1050.
Applications of the harmonic series and its partial sums include Euler's proof that there are infinitely many prime numbers, the analysis of the coupon collector's problem on how many random trials are needed to provide a complete range of responses, the connected components of random graphs, the block-stacking problem on how far over the edge ...
Postal rates to 1847. Initial United States postage rates were set by Congress as part of the Postal Service Act signed into law by President George Washington on February 20, 1792. The postal rate varied according to "distance zone", the distance a letter was to be carried from the post office where it entered the mail to its final destination.
XYZ Ltd. issues a bond with a $1000 face value and a $980 published price, with a coupon rate of 5% paid semi-annually and a maturity date of five years. The annual coupon payment is 5% of $1000, or $50. The investor receives a $25 coupon payment every six months until the maturity date. In this case, $980 is the clean price of the bond.
Graphs of n vs E(T) in the coupon collector's problem: Image title: Graphs of the number of coupons, n vs the expected number of tries to collect them, E(T) = ceiling(n H(n)) in the coupon collector's problem, drawn by CMG Lee. Width: 100%: Height: 100%