Quiz 14 - FDA

11/2/23, 4:01 PM Quiz 14 localhost:8889/nbconvert/html/Downloads/Quiz 14.ipynb?download=false 1/8 <class 'pandas.core.frame.DataFrame'> RangeIndex: 1000 entries, 0 to 999 Data columns (total 1 columns): # Column Non-Null Count Dtype --- ------ -------------- ----- 0 Number of Tests 1000 non-null int64 dtypes: int64(1) memory usage: 7.9 KB In [1]: # Importing necessary libraries import pandas as pd import numpy as np import matplotlib.pyplot as plt # Generating the dataset np . random . seed ( 42 ) r = 3 # Number of failures p = 0.2 # Probability of failure data = np . random . negative_binomial ( r , p , 1000 ) # Generating data using negative binomial distribution df = pd . DataFrame ( data , columns = [ 'Number of Tests' ]) # Display the first few rows of the dataframe df . head () Out[1]: In [2]: df . info () In [3]: df . describe ()

11/2/23, 4:01 PM Quiz 14 localhost:8889/nbconvert/html/Downloads/Quiz 14.ipynb?download=false 2/8 Out[3]: In [4]: # Plotting the histogram plt . figure ( figsize = ( 10 , 6 )) plt . hist ( df [ 'Number of Tests' ], bins = 20 , color = 'skyblue' , edgecolor = 'black' ) plt . title ( 'Distribution of Number of Tests Before Failure' , fontsize = 15 ) plt . xlabel ( 'Number of Tests' , fontsize = 12 ) plt . ylabel ( 'Frequency' , fontsize = 12 ) plt . grid ( axis = 'y' , alpha = 0.75 ) plt . show ()

11/2/23, 4:01 PM Quiz 14 localhost:8889/nbconvert/html/Downloads/Quiz 14.ipynb?download=false 4/8 Estimated value of p: 0.21278292066823185 Probability of a device failing after more than 5 tests: 0.7681287870549661 In [7]: from scipy.stats import nbinom # Calculating the probability of failure after more than 5 tests prob_more_than_5_tests = nbinom . sf ( 5 , r , p_estimated ) print ( "Estimated value of p:" , p_estimated ) print ( "Probability of a device failing after more than 5 tests:" , prob_more_than_5_tests ) In [8]: # Importing necessary libraries import pandas as pd import numpy as np import matplotlib.pyplot as plt from scipy.stats import gamma # Generating the dataset using Gamma Distribution np . random . seed ( 42 ) shape_parameter = 2 scale_parameter = 800 # Mean = shape * scale = 1600 data = np . random . gamma ( shape_parameter , scale_parameter , 1000 ) df_2 = pd . DataFrame ( data , columns = [ 'Lifetime in Hours' ]) # Display the first few rows of the dataframe df_2 . head ()

11/2/23, 4:01 PM Quiz 14 localhost:8889/nbconvert/html/Downloads/Quiz 14.ipynb?download=false 5/8 Out[8]: In [9]: df_2 Out[9]: In [10]: df_2 . info ()

11/2/23, 4:01 PM Quiz 14 localhost:8889/nbconvert/html/Downloads/Quiz 14.ipynb?download=false 7/8 plt . ylabel ( 'Frequency' , fontsize = 12 ) plt . grid ( axis = 'y' , alpha = 0.75 ) plt . show () In [14]: # Calculating the sample mean and variance mean_data_2 = np . mean ( data ) var_data_2 = np . var ( data )

11/2/23, 4:01 PM Quiz 14 localhost:8889/nbconvert/html/Downloads/Quiz 14.ipynb?download=false 8/8 Estimated shape parameter: 2.1583043230324153 Estimated scale parameter: 763.5365389883217 Probability of a light bulb lasting more than 2000 hours: 0.3018148050158612 # Estimating the shape and scale parameters shape_estimated_2 = mean_data_2 ** 2 / var_data_2 scale_estimated_2 = var_data_2 / mean_data_2 # Calculating the probability of a light bulb lasting more than 2000 hours prob_more_than_2000_hours_2 = 1 - gamma . cdf ( 2000 , a = shape_estimated_2 , scale = scale_estimated_2 ) print ( "Estimated shape parameter:" , shape_estimated_2 ) print ( "Estimated scale parameter:" , scale_estimated_2 ) print ( "Probability of a light bulb lasting more than 2000 hours:" , prob_more_than_2000_hours_2 )