Fibonacci and the Pythagorean Problem 3. For any 6.3 Problems or F P+1 the prim 1. It can be established that each positive integer is representable as a sum of Fibonacci numbers, none taken more than once; for example, 4. From th that con prime. 5 = F3 + F4, 5. One car Fibonac 6 F1+ F3+ F4, specific 7=F1+ F2+ F3 + F4. gcd Write the integers 50, 75, 100, and 125 in this manner. Verify gcd(F1 Show that the sum of the first n Fibonacci (a) 2. numbers with odd indices is given by the formula 6. Use Pr F1+F3+ F5 + F2n-1 F2n only if CLST [Hint: Add the equalities F1 F2, F3 = F4- F2, Fs F6- Fa, ... .] (b) Show that the sum of the first n Fibonacci numbers with even indices is given by the 7. Establi 1 (a) 2 (b) 3 (c) (d) S formula 2U 1s F2+ F4+F6+ ..+F2n [Hint: = F2n+1 - 1. proble [Hint: Use part (a) and the identity FI+F2+ F3 + . + Fan = F2n+2 -- 1.} C Obtain the following formula for the altermaing um of Fibonacci numbers: 8 Show Fibon +(1)"+ Fi-F2 + F3- F4+ Wis = (-1)"+1 Fn-1 + 1.

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Contingency Table

A contingency table can be defined as the visual representation of the relationship between two or more categorical variables that can be evaluated and registered. It is a categorical version of the scatterplot, which is used to investigate the linear relationship between two variables. A contingency table is indeed a type of frequency distribution table that displays two variables at the same time.

Binomial Distribution

Binomial is an algebraic expression of the sum or the difference of two terms. Before knowing about binomial distribution, we must know about the binomial theorem.