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@arvin

Dont have key.

it can be done in different ways but i am using here hit and trial as that can be lengthy....

note: non decreasing(for a0,a1) means a0<=a1

consider it for single symbol : <a0>

non decreasing sequence= (0), (1),(2) = 3sequence

total sequence possible = 3( ao can contain 0,1,2)

probability(1symbol) = 3/3 =1 [email protected]

now consider it for two symbol sequence : <a0,a1>

so non decreasing sequence will be : (0,0) , (0,1) , (0,2) ,(1,1) ,(1,2) ,(2,2) =6

total sequences from 3 symbols = 3*3 (a0 can take 3values = 0,1,2 also a1)

probability(2 symbols)= 6/9 =2/3...[email protected]

similarly for three symbols <a0,a1,a2>

non decreasing sequence= (0,0,0), (0,0,1), (0,0,2), (0,1,1), (0,1,2), (0,2,2) ,(1,1,1), (1,1,2) ,(1,2,2), (2,2,2)=10sequences

total sequences = 3*3*3

probability(3 symbols) = 10/27 [email protected]

checking option A for above case :

(n=1) = (1+3*1 +2)/(2 *3) = 6/6 =1 [email protected] proved

(n=2) = (2*2+ 3*2 +2) / (2*3*3) = 12/18 = 2/[email protected] proved

(n=3) = (3*3 +3*3 +2)/(2*3*3*3)=20/54=10/[email protected] proved.

by

@MiNiPanda

I ll try that but solving equations, especially non homogeneous is a bit booring task :p

Help me with denominator part from options

@minipanda the equation will become : x3-2x2+x-1 =0

but how to solve this..

@arvin

Actually , for homogeneous part ,equation becomes "r^2 -2r+1".

Find its roots, then find solution for homogeneous part.

Then solve for non homogeneous part.

A bit lengthy process.

https://www.tutorialspoint.com/discrete_mathematics/discrete_mathematics_recurrence_relation.htm

This will help or there are YouTube vid.

Lets Tn be total no of non decreasing sequence possible.

and 3n be the total no. of sequence possible.

Hence probability be Tn / 3n .

Tn can be calculated in following ways

1 vote