Data Science and Machine Learning (Theory and Projects) A to Z - Random Variables: Binomial Python Practice

The video tutorial explores the concept of distributions, focusing on geometric and binomial random variables. It discusses the use of histograms to visualize distributions and the importance of defining the number of bins for detailed analysis. The tutorial then introduces binomial trials, explaining how to implement them using loops and vectorization with Numpy for efficiency. It further analyzes the distribution of binomial trials, demonstrating how changes in probability affect the distribution's shape, highlighting the symmetric nature around the mean.

What is the purpose of defining the number of bins in a histogram?

• To increase the height of the bars

• To see more detailed data spread

• To adjust the width of the bars

• To change the color of the histogram

What are the two values accepted by a binomial trial?

• Number of trials and number of failures

• Number of Bernoulli trials and probability of success

• Number of successes and number of failures

• Probability of failure and number of successes

Why is a vectorized implementation preferred over a loop for binomial trials?

• It is easier to understand

• It produces more accurate results

• It is more efficient and faster

• It uses less memory

What happens to the number of heads when the probability of success is decreased?

• The number of heads increases

• The number of heads remains the same

• The number of heads decreases

• The number of heads becomes zero

What is the effect of increasing the number of Bernoulli trials on the distribution?

• The distribution becomes narrower

• The distribution becomes smoother

• The distribution becomes wider

• The distribution becomes more jagged

What shape does the binomial distribution take as the number of trials increases?

• A zigzag pattern

• A bell curve

• A straight line

• A flat line

What is the expected number of heads when the probability of success is 0.5 in 1000 trials?

• 750 heads

• 250 heads

• 500 heads

• 100 heads

How does the peak of the binomial distribution shift when the probability of success is increased to 0.9?

• The peak shifts to the right

• The peak shifts to the left

• The peak disappears

• The peak remains in the center

What happens to the binomial distribution when the probability of success is very low?

• The distribution becomes uniform

• The peak shifts to the right

• The peak shifts to the left

• The distribution becomes skewed

What characteristic of the binomial distribution is maintained even when the probability of success changes?

• The distribution becomes asymmetric

• The distribution becomes skewed

• The distribution remains symmetric

• The distribution becomes random