Зміст курсу
Probability Theory Update
Probability Theory Update
Probability Mass Function (PMF) 2/2
Probability mass function over a range:
In some cases, we want to know the probability that discrete random variables are equal to numbers over a range.
Example:
Calculate the probability that we will have success with the fair coin at 4 or less times (0, 1, 2, 3 or 4) (the chance of getting head or tail is 50%) if we have 15 attempts. We assume that success means getting a head.
Python realization:
# Import required library import scipy.stats as stats # The probability of getting 0 successes prob_0 = stats.binom.pmf(0, n = 15, p = 0.5) # The probability of getting 1 success prob_1 = stats.binom.pmf(1, n = 15, p = 0.5) # The probability of getting 2 successes prob_2 = stats.binom.pmf(2, n = 15, p = 0.5) # The probability of getting 3 successes prob_3 = stats.binom.pmf(3, n = 15, p = 0.5) # The probability of getting 4 successes prob_4 = stats.binom.pmf(4, n = 15, p = 0.5) # The resulting probability probability = prob_0 + prob_1 + prob_2 + prob_3 + prob_4 print("The probability is", probability * 100, "%")
Explanation
We've found the probability that a discrete random variable will equal exactly 0, 1, 2, 3, or 4 using the probability mass function. Then, we summed up all probabilities using the addition rule because each of the found outcomes was permissible for us.
Перейдіть на комп'ютер для реальної практикиПродовжуйте з того місця, де ви зупинились, використовуючи один з наведених нижче варіантівДякуємо за ваш відгук!
Probability Mass Function (PMF) 2/2
Probability mass function over a range:
In some cases, we want to know the probability that discrete random variables are equal to numbers over a range.
Example:
Calculate the probability that we will have success with the fair coin at 4 or less times (0, 1, 2, 3 or 4) (the chance of getting head or tail is 50%) if we have 15 attempts. We assume that success means getting a head.
Python realization:
# Import required library import scipy.stats as stats # The probability of getting 0 successes prob_0 = stats.binom.pmf(0, n = 15, p = 0.5) # The probability of getting 1 success prob_1 = stats.binom.pmf(1, n = 15, p = 0.5) # The probability of getting 2 successes prob_2 = stats.binom.pmf(2, n = 15, p = 0.5) # The probability of getting 3 successes prob_3 = stats.binom.pmf(3, n = 15, p = 0.5) # The probability of getting 4 successes prob_4 = stats.binom.pmf(4, n = 15, p = 0.5) # The resulting probability probability = prob_0 + prob_1 + prob_2 + prob_3 + prob_4 print("The probability is", probability * 100, "%")
Explanation
We've found the probability that a discrete random variable will equal exactly 0, 1, 2, 3, or 4 using the probability mass function. Then, we summed up all probabilities using the addition rule because each of the found outcomes was permissible for us.
Перейдіть на комп'ютер для реальної практикиПродовжуйте з того місця, де ви зупинились, використовуючи один з наведених нижче варіантівДякуємо за ваш відгук!
Probability Mass Function (PMF) 2/2
Probability mass function over a range:
In some cases, we want to know the probability that discrete random variables are equal to numbers over a range.
Example:
Calculate the probability that we will have success with the fair coin at 4 or less times (0, 1, 2, 3 or 4) (the chance of getting head or tail is 50%) if we have 15 attempts. We assume that success means getting a head.
Python realization:
# Import required library import scipy.stats as stats # The probability of getting 0 successes prob_0 = stats.binom.pmf(0, n = 15, p = 0.5) # The probability of getting 1 success prob_1 = stats.binom.pmf(1, n = 15, p = 0.5) # The probability of getting 2 successes prob_2 = stats.binom.pmf(2, n = 15, p = 0.5) # The probability of getting 3 successes prob_3 = stats.binom.pmf(3, n = 15, p = 0.5) # The probability of getting 4 successes prob_4 = stats.binom.pmf(4, n = 15, p = 0.5) # The resulting probability probability = prob_0 + prob_1 + prob_2 + prob_3 + prob_4 print("The probability is", probability * 100, "%")
Explanation
We've found the probability that a discrete random variable will equal exactly 0, 1, 2, 3, or 4 using the probability mass function. Then, we summed up all probabilities using the addition rule because each of the found outcomes was permissible for us.
Перейдіть на комп'ютер для реальної практикиПродовжуйте з того місця, де ви зупинились, використовуючи один з наведених нижче варіантівДякуємо за ваш відгук!
Probability mass function over a range:
In some cases, we want to know the probability that discrete random variables are equal to numbers over a range.
Example:
Calculate the probability that we will have success with the fair coin at 4 or less times (0, 1, 2, 3 or 4) (the chance of getting head or tail is 50%) if we have 15 attempts. We assume that success means getting a head.
Python realization:
# Import required library import scipy.stats as stats # The probability of getting 0 successes prob_0 = stats.binom.pmf(0, n = 15, p = 0.5) # The probability of getting 1 success prob_1 = stats.binom.pmf(1, n = 15, p = 0.5) # The probability of getting 2 successes prob_2 = stats.binom.pmf(2, n = 15, p = 0.5) # The probability of getting 3 successes prob_3 = stats.binom.pmf(3, n = 15, p = 0.5) # The probability of getting 4 successes prob_4 = stats.binom.pmf(4, n = 15, p = 0.5) # The resulting probability probability = prob_0 + prob_1 + prob_2 + prob_3 + prob_4 print("The probability is", probability * 100, "%")
Explanation
We've found the probability that a discrete random variable will equal exactly 0, 1, 2, 3, or 4 using the probability mass function. Then, we summed up all probabilities using the addition rule because each of the found outcomes was permissible for us.
Перейдіть на комп'ютер для реальної практикиПродовжуйте з того місця, де ви зупинились, використовуючи один з наведених нижче варіантівПерейдіть на комп'ютер для реальної практикиПродовжуйте з того місця, де ви зупинились, використовуючи один з наведених нижче варіантів