Binomial distribution in SciPy - Cheat Sheet & Quick Revision

Recall & Review

beginner

What is a Binomial distribution?

A Binomial distribution shows the chance of getting a certain number of successes in a fixed number of tries, where each try has two possible outcomes (like success or failure) and the chance of success stays the same each time.

beginner

What are the two main parameters of a Binomial distribution?

The two main parameters are:<br>1. Number of trials (n): How many times you try.<br>2. Probability of success (p): The chance of success in each try.

intermediate

How do you calculate the probability of exactly k successes in n trials using scipy?

Use scipy.stats.binom.pmf(k, n, p). It gives the probability of getting exactly k successes out of n tries with success chance p.

intermediate

What does the cumulative distribution function (CDF) tell us in a Binomial distribution?

The CDF gives the chance of getting up to k successes (that is, k or fewer) in n trials. In scipy, use scipy.stats.binom.cdf(k, n, p).

beginner

Why is the Binomial distribution useful in real life?

It helps us understand situations with yes/no outcomes repeated many times, like flipping coins, checking if a light bulb works, or if a customer buys a product.

Which of these is NOT a parameter of the Binomial distribution?

A Number of trials (n)

B Probability of success (p)

C Mean of the distribution

D Number of successes (k)

The mean is a result calculated from the distribution, not a parameter you set. The parameters are number of trials (n) and probability of success (p).

What does binom.pmf(3, 10, 0.5) calculate?

A Probability of 3 or fewer successes in 10 trials

B Probability of exactly 3 successes in 10 trials with 50% success chance

C Probability of more than 3 successes in 10 trials

D Expected number of successes

The pmf function gives the probability of exactly k successes, here k=3.

If the probability of success is 0.7, what is the probability of failure in one trial?

A Cannot be determined

B 0.7

C 1.7

D 0.3

Probability of failure is 1 minus the probability of success, so 1 - 0.7 = 0.3.

Which scipy function gives the chance of getting up to k successes?

A binom.cdf()

B binom.var()

C binom.mean()

D binom.pmf()

The cumulative distribution function (cdf) gives the probability of k or fewer successes.

In a Binomial distribution, what does 'n' represent?

A Number of trials

B Number of successes

C Probability of success

D Probability of failure

'n' is the total number of trials or attempts.

Explain the Binomial distribution and its key parameters in your own words.

Think about repeated yes/no experiments like coin flips.

Describe how you would use scipy to find the probability of getting exactly 4 successes in 15 trials with a 0.3 success chance.

Remember pmf means probability mass function.