This thesis will focus on generating the probability mass function using Fibonacci sequenceas the coefficient of the power series. The discrete probability, named Fibonacci distribution,was formed by taking into consideration the recursive property of the Fibonacci sequence,the radius of convergence of the power series, and additive property of mutually exclusiveevents. This distribution satisfies the requisites of a legitimate probability mass function. It's cumulative distribution function and the moment generating function are then derived and the latter are used to generate moments of the distribution, specifically, the mean and the variance. The characteristics of some convergent sequences generated from the Fibonacci sequenceare found useful in showing that the limiting form of the Fibonacci distribution is a geometricdistribution. Lastly, the paper showcases applications and simulations of the Fibonacci distribution using MATLAB. / <p></p><p></p><p></p>
| Identifer | oai:union.ndltd.org:UPSALLA1/oai:DiVA.org:umu-201552 |
| Date | January 2022 |
| Creators | Amanuel, Meron |
| Publisher | Umeå universitet, Institutionen för matematik och matematisk statistik |
| Source Sets | DiVA Archive at Upsalla University |
| Language | English |
| Detected Language | English |
| Type | Student thesis, info:eu-repo/semantics/bachelorThesis, text |
| Format | application/pdf |
| Rights | info:eu-repo/semantics/openAccess |
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