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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:


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# 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.

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Sección 4. Capítulo 5

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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.

Cambia al escritorio para practicar en el mundo realContinúe desde donde se encuentra utilizando una de las siguientes opciones

¿Todo estuvo claro?

¡Gracias por tus comentarios!

Sección 4. Capítulo 5

Cambia al escritorio para practicar en el mundo realContinúe desde donde se encuentra utilizando una de las siguientes opciones