Binomial and Geometric Random Variables

The video tutorial covers binomial and geometric random variables, explaining their differences, conditions, and applications. It details the binomial distribution, including how to calculate probabilities using binomial PDF and CDF. The tutorial also introduces geometric random variables, focusing on counting trials until the first success, and explains the geometric distribution and its calculations.

What is the primary difference between binomial and geometric random variables?

• Binomial counts successes in fixed trials; geometric counts trials until first success.

• Binomial counts failures; geometric counts successes.

• Binomial is continuous; geometric is discrete.

• Binomial uses normal distribution; geometric uses exponential distribution.

Which of the following is NOT a condition for a binomial setting?

• Fixed number of trials

• Independent trials

• Variable probability of success

• Binary outcomes

In a binomial distribution, what does 'n choose k' represent?

• The probability of k successes

• The number of ways to arrange k successes in n trials

• The expected number of successes

• The standard deviation of the distribution

How do you calculate the mean of a binomial distribution?

• p divided by n

• n divided by p

• Square root of n times p

• n times p

What is the main focus of a geometric random variable?

• Calculating the variance of outcomes

• Measuring the probability of failure

• Counting the number of trials until the first success

• Counting the number of successes in a fixed number of trials

How is the expected value of a geometric random variable calculated?

• 1 divided by the probability of success

• Probability of success times number of trials

• Square root of the number of trials

• Probability of failure divided by number of trials