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Develop a Poker test for four digit numbers

Poker test is used to test independence property of a random numbers on the basic of similarity of digits.

Step 1: $H_0: R_i$~ Independently

$H_1: R_i$~is not independently

Step 2: N=?

Step 3: generate frequency distributor table

Step 4: $χ_i^2$=$∑(O_i-E_i)^2/E_i$

Step 5: If : $(χ_{α,k-1})^2\lt = χ_0^2$ then accept $H_0$ else reject $H_0$.

Note: This test works for only up to 3 decimal places if not we have to convert number into 3 decimal number.

Consider an example : A sequence of 1 thousand 3 digits Random numbers have been generated and analysis indicates that 560 have three different digits 380 contains exactly one pair of like digits, 60 contains three like digits based on poker test check independence property of random numbers.

Solution:

Step 1: $H_0: R_i$~ Independently

$H_1: R_i$~is not independently

Step 2: N=1000

Step 3: generate frequency distributor table

Step 4: $χ_i^2$=$∑(O_i-E_i)^2/E_i$ =96.36

step 5: $(χ_{α,k-1})^2$ = 5.99

Step 5: If : $(χ_{α,k-1})^2\lt = χ_0^2$ hence accept $H_0$