Difference between n and size parameters in np.random.binomial (n, p, size = 1000)

Question

I could not understand the difference between n and size parameters in np.random.binomial.

N = 1200 p =0.53 q = 1000 np.random.binomial(N, p, size = q) np.random.binomial(1, p, size = q) np.random.binomial(N,p, size= q) 

N is the number of tests, but this is what size does in the above formula. also kindly explain the three versions of binomes.

Answer 1

• np.random.binomial (N, p, size = q)
• np.random.binomial (1, p, size = q)
• np.random.binomial (N, p, size = q)

1st and 3rd are similar, I see. These two are binomial random number generators.

And, the second is a Bernoulli random number generator

---

Binom Explanation:

A binomial random variable calculates how often a particular event occurs in a fixed number of attempts or trials.

Here

• n = number of tests
• p = probable event of interest occurs in any trial
• size = the number of times you want to run this experiment.

Suppose you want to check how many times you get six if you roll dice 10 times. Here

• n = 10
• p = (1/6) # probability of getting six in each roll

But, you have to do this experiment several times.

Let, in the first experiment you get 3 six

In the 2nd experiment you get 2 six

In the third experiment you get 2 six

In the Pth experiment, you get 2 six, here P is the size

---

Bernoulli explanation:

Suppose you are performing an experiment with two possible outcomes: either success or failure. Success happens with probability p, while probability 1-p fails. The random variable, which takes the value 1 in case of success and 0 in case of failure, is called the Bernoulli random variable.

Here

• n = 1 because you need to check if it will be success or failure once
• p = probability of success
• size = number of times you check this

---

You can also read this, numpy.random.binomial

Also, the difference between Binomial and Bernoulli

Answer 2

n and p describe the distribution itself. size gives the number (and shape) of the results. Best illustrated in this example from the manual:

 >>> n, p = 10, .5 # number of trials, probability of each trial >>> s = np.random.binomial(n, p, 1000) # result of flipping a coin 10 times, tested 1000 times. 

You will receive a vector with 1000 numbers, each of which will be a binonymous distribution (10, 0.5).

Answer 3

In probability theory and statistics, a binomial distribution with parameters n and p is a discrete probability distribution of the number of successes (which is the output of the np.random.binomial function when testing 1 time) into a sequence of n independent experiments (which is equal to n in your formula) , each of which the question “yes - no” is asked, and each with its own logical meaning: success / yes / true / one (with probability p) or error / no / false / zero (with probability q = 1 - p).
A test is nothing more than how many times we want to run this experiment, test = 10 will generate 10 output- (everything represents a different “no time, getting yes”)