Cumulative Distribution Function (CDF) 2/2
Probability mass function over a range:
In some cases, we want to know the probability that a random variable is equal to numbers over a range.
Formula:
P(a < X <= b) = Fx(a) - Fx(b)
- P(a < X <= b) - the probability that a random variable X takes a value within the rage (a; b].
- Fx(a) - applying CMT to find a probability that a random variable X takes a value less than or a.
- Fx(b) - applying CMT to find a probability that a random variable X takes a value less than or b.
Example:
Calculate the probability a fair coin will succed in no more than 8 but no less than 4 cases (4; 8] if we have 15 attempts. We assume that success means getting a head.
Python realization:
12345678910111213141516171819# Import required library import scipy.stats as stats # The probability of getting 8 successes prob_8 = stats.binom.pmf(8, n = 15, p = 0.5) # The probability of getting 4 success prob_4 = stats.binom.pmf(4, n = 15, p = 0.5) # The resulting probability probability = prob_8 - prob_4 print("The probability is", probability * 100, "%")
Explanation
According to the formula, we subtract the probability that a random variable will take a value less than or four from the probability that a random value will take a value less than or 8.
Tak for dine kommentarer!
single
Spørg AI
Spørg AI
Spørg om hvad som helst eller prøv et af de foreslåede spørgsmål for at starte vores chat
Awesome!
Completion rate improved to 3.7Cumulative Distribution Function (CDF) 2/2
Stryg for at vise menuen
Probability mass function over a range:
In some cases, we want to know the probability that a random variable is equal to numbers over a range.
Formula:
P(a < X <= b) = Fx(a) - Fx(b)
- P(a < X <= b) - the probability that a random variable X takes a value within the rage (a; b].
- Fx(a) - applying CMT to find a probability that a random variable X takes a value less than or a.
- Fx(b) - applying CMT to find a probability that a random variable X takes a value less than or b.
Example:
Calculate the probability a fair coin will succed in no more than 8 but no less than 4 cases (4; 8] if we have 15 attempts. We assume that success means getting a head.
Python realization:
12345678910111213141516171819# Import required library import scipy.stats as stats # The probability of getting 8 successes prob_8 = stats.binom.pmf(8, n = 15, p = 0.5) # The probability of getting 4 success prob_4 = stats.binom.pmf(4, n = 15, p = 0.5) # The resulting probability probability = prob_8 - prob_4 print("The probability is", probability * 100, "%")
Explanation
According to the formula, we subtract the probability that a random variable will take a value less than or four from the probability that a random value will take a value less than or 8.
Skift til skrivebord for at øve i den virkelige verdenFortsæt der, hvor du er, med en af nedenstående mulighederTak for dine kommentarer!
Awesome!
Completion rate improved to 3.7single
