Question

Which standard library function returns a random integer within a specified range of values?

1) randint()
2) random()
3) randrange()
4) choice()

Answer 1

The function that returns a random integer within a specified range is 'randint()'. It is used to simulate binomial distributions by being called multiple times and summing the outcomes to represent the number of successes in a number of trials.

Step-by-step explanation:

The standard library function that returns a random integer within a specified range is randint(), which is the first option presented in the question. To simulate a binomial distribution, you can use the randint function in a programmable calculator or a programming language such as Python. You would call randint(0, 1) to perform a trial, where '0' might represent failure and '1' might represent success, and each trial has a 50% chance of success.

To simulate 10 observations of the random variable indicating the number of successes in five trials, you would repeatedly call randint(0, 1) five times for each observation and sum the results. This whole process should be repeated 10 times to obtain your 10 observations of the random variable.

The values that the random variable may take on range from 0 (no successes in five trials) to 5 (all trials are successful). The distribution for X is binomial since the number of trials is fixed, each trial is independent, and each trial has only two possible outcomes (success or failure).