




from math import factorial



def       UpperCAmelCase       (     _snake_case						, _snake_case						, _snake_case							):


							if successes > trials:
														raise ValueError('''successes must be lower or equal to trials'''							)
							if trials < 0 or successes < 0:
														raise ValueError('''the function is defined for non-negative integers'''							)
							if not isinstance(_lowerCamelCase						, _lowerCamelCase							) or not isinstance(_lowerCamelCase						, _lowerCamelCase							):
														raise ValueError('''the function is defined for non-negative integers'''							)
							if not 0 < prob < 1:
														raise ValueError('''prob has to be in range of 1 - 0'''							)
							lowerCAmelCase   =		(prob**successes) * ((1 - prob) ** (trials - successes))
							# Calculate the binomial coefficient: n! / k!(n-k)!
							lowerCAmelCase   =		float(factorial(_lowerCamelCase							)							)
							coefficient /= factorial(_lowerCamelCase							) * factorial(trials - successes							)
							return probability * coefficient


if __name__ == "__main__":
		from doctest import testmod

		testmod()
		print("""Probability of 2 successes out of 4 trails""")
		print("""with probability of 0.75 is:""", end=""" """)
		print(binomial_distribution(2, 4, 0.75))





import torch

from diffusers import StableDiffusionPipeline


UpperCAmelCase_						="""path-to-your-trained-model"""
UpperCAmelCase_						=StableDiffusionPipeline.from_pretrained(model_id, torch_dtype=torch.floataa).to("""cuda""")

UpperCAmelCase_						="""A photo of sks dog in a bucket"""
UpperCAmelCase_						=pipe(prompt, num_inference_steps=50, guidance_scale=7.5).images[0]

image.save("""dog-bucket.png""")



