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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Sektion 4. Kapitel 5

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.

Skift til skrivebord for at øve i den virkelige verdenFortsæt der, hvor du er, med en af nedenstående muligheder

Var alt klart?

Tak for dine kommentarer!

Sektion 4. Kapitel 5

Skift til skrivebord for at øve i den virkelige verdenFortsæt der, hvor du er, med en af nedenstående muligheder