Syntax error Python Program to calculate function from indicator random variable from given condition

Python Program to calculate function from indicator random variable from given condition

Suppose we have two values k and n. Consider a random permutation say p1, p2, ..., pn of first n natural numbers numbers 1, 2, ..., n and calculate the value F, such that F = (X2+...+Xn-1)k, where Xi is an indicator random variable, which is 1 when one of the following two conditions holds: pi-1 < pi > pi+1 or pi-1 > pi < pi+1 and Xi is 0 otherwise. We have to find the expected value of F.

So, if the input is like k = 1 n = 1000, then the output will be 1996/3

To solve this, we will follow these steps −

  • Define a function exp_factor() . This will take n,k
  • if k is same as 1, then
    • return(2*(n-2) , 3)
  • otherwise when k is same as 2, then
    • return (40*n^2 -144*n + 131, 90)
  • otherwise when k is same as 3, then
    • return (280*n^3 - 1344*n^2 +2063*n -1038,945)
  • otherwise when k is same as 4, then
    • return (2800*n^4 - 15680*n^3 + 28844*n^2 - 19288*n + 4263, 14175)
  • otherwise when k is same as 5, then
    • return (12320*n^5 - 73920*n^4 + 130328*n^3 - 29568*n^2 - 64150*n -5124, 93555)
  • return 1.0
  • From the main method, do the following −
  • M := n-2
  • p := 2.0/3
  • q := 1 - p
  • (num, den) := exp_factor(n, k)
  • g := gcd(num, den)
  • return fraction (num/g) / (den/g)

Example

Let us see the following implementation to get better understanding −

from math import gcd

def exp_factor(n,k):
   if k == 1:
      return (2*(n-2),3)
   elif k == 2:
      return (40*n**2 -144*n + 131,90)
   elif k == 3:
      return (280*n**3 - 1344*n**2 +2063*n -1038,945)
   elif k == 4:
      return (2800*n**4 - 15680*n**3 + 28844*n**2 - 19288*n + 4263, 14175)
   elif k == 5:
      return (12320*n**5 - 73920*n**4 + 130328*n**3 - 29568*n**2 - 64150*n -5124, 93555)
   return 1.0

def solve(k, n):
   M = n-2
   p = 2.0/3
   q = 1 - p

   num, den = exp_factor(n,k)
   g = gcd(num, den)
   return str(int(num/g))+'/'+str(int(den/g))

k = 1
n = 1000
print(solve(k, n))

Input

1, 1000

Output

1996/3
Updated on: 2021-10-11T11:22:04+05:30

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