Python 3.8, 52 50 bytes

-2 bytes inspired by EasyasPi's answer.

Produces some integers with probability \$\frac 2 {256}\$ and some with probability \$\frac 3 {256}\$ in each iteration. Output includes a trailing .0 for each number.

import os while id:print(id:=os.urandom(1)[0]%100) 

Try it online!

Uses the builtin function id to avoid assigning a new variable before the loop.
os.urandom(size) returns a bytes object with size random bytes. The bytes object behaves quite similar to a list of integers, which means os.urandom(1)[0] gives a single random integer from \$[0,255]\$, which we map to an integer from \$[0,99]\$ with a modulo operation.

Python 3.8, 53 bytes

Generates integers from a uniform distribution over \$[0, 99]\$.

from random import* while id:print(id:=randint(0,99)) 

Try it online!

Python 3.8, 52 50 bytes

-2 bytes inspired by EasyasPi's answer.

Produces some integers with probability \$\frac 2 {256}\$ and some with probability \$\frac 3 {256}\$ in each iteration.

import os while id:print(id:=os.urandom(1)[0]%100) 

Try it online!

Uses the builtin function id to avoid assigning a new variable before the loop.
os.urandom(size) returns a bytes object with size random bytes. The bytes object behaves quite similar to a list of integers, which means os.urandom(1)[0] gives a single random integer from \$[0,255]\$, which we map to an integer from \$[0,99]\$ with a modulo operation.

Python 3.8, 53 bytes

Generates integers from a uniform distribution over \$[0, 99]\$.

from random import* while id:print(id:=randint(0,99)) 

Try it online!

Python 3.8, 52 bytes

Produces some integers with probability \$\frac 2 {256}\$ and some with probability \$\frac 3 {256}\$ in each iteration. Output includes a trailing .0 for each number.

import os while id:print(id:=os.urandom(1)[0]//2.56) 

Try it online!

Uses the builtin function id to avoid assigning a new variable before the loop.
os.urandom(size) returns a bytes object with size random bytes. The bytes object behaves quite similar to a list of integers, which means os.urandom(1)[0] gives a single random integer from \$[0,255]\$, which we scale with floor division by \$2.56\$.

Python 3.8, 53 bytes

Generates integers from a uniform distribution over \$[0, 99]\$.

from random import* while id:print(id:=randint(0,99)) 

Try it online!

Python 3.8, 52 50 bytes

-2 bytes inspired by EasyasPi's answer.

Produces some integers with probability \$\frac 2 {256}\$ and some with probability \$\frac 3 {256}\$ in each iteration. Output includes a trailing .0 for each number.

import os while id:print(id:=os.urandom(1)[0]%100) 

Try it online!

Uses the builtin function id to avoid assigning a new variable before the loop.
os.urandom(size) returns a bytes object with size random bytes. The bytes object behaves quite similar to a list of integers, which means os.urandom(1)[0] gives a single random integer from \$[0,255]\$, which we map to an integer from \$[0,99]\$ with a modulo operation.

Python 3.8, 53 bytes

Generates integers from a uniform distribution over \$[0, 99]\$.

from random import* while id:print(id:=randint(0,99)) 

Try it online!

Python 3.8, 52 bytes

Produces some integers with probability \$\frac 2 {256}\$ and some with probability \$\frac 3 {256}\$ in each iteration. Output includes a trailing .0 for each number.

import os while id:print(id:=os.urandom(1)[0]//2.56) 

Try it online!

Uses the builtin function id to avoid assigning a new variable before the loop.
os.urandom(size) returns a bytes object with size random bytes. The bytes object behaves quite similar to a list of integers, which means os.urandom(1)[0] gives a single random integer from \$[0,255]\$, which we scale with floor division by \$2.56\$.

Python 3.8, 53 bytes

Generates integers from a uniform distribution over \$[0, 99]\$.

from random import* while id:print(id:=randrange(99)) 

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There are a few alternatives for generating the random numbers: randrange(99) could be replaced by randint(0,99) at the same length and secrets.randbelow would be two bytes longer.

Python 3.8, 52 bytes

Produces some integers with probability \$\frac 2 {256}\$ and some with probability \$\frac 3 {256}\$ in each iteration. Output includes a trailing .0 for each number.

import os while id:print(id:=os.urandom(1)[0]//2.56) 

Try it online!

Uses the builtin function id to avoid assigning a new variable before the loop.
os.urandom(size) returns a bytes object with size random bytes. The bytes object behaves quite similar to a list of integers, which means os.urandom(1)[0] gives a single random integer from \$[0,255]\$, which we scale with floor division by \$2.56\$.

Python 3.8, 53 bytes

Generates integers from a uniform distribution over \$[0, 99]\$.

from random import* while id:print(id:=randint(0,99)) 

Try it online!