Bernoulli Distribution Concepts

The lecture introduces the Bernoulli distribution, explaining its definition and the types of events it models, such as coin flips and binary decisions. It covers the graphical representation of the distribution, expected value, and variance. An example of an unfair coin is used to illustrate these concepts, showing how the expected value and variance are calculated.

What does the notation 'Bern(p)' signify in the context of Bernoulli distribution?

• A Poisson distribution with rate p

• A binomial distribution with n trials and probability p

• A normal distribution with mean p

• A Bernoulli distribution with probability of success p

Which of the following is an example of an event that follows a Bernoulli distribution?

• Choosing a random number between 1 and 10

• Drawing a card from a deck

• Flipping a coin

• Rolling a six-sided die

How many possible outcomes are there in a Bernoulli distribution?

• Four

• Three

• Two

• One

In a Bernoulli distribution graph, what do the two bars represent?

• The mode and range

• The standard deviation and variance

• The probability of success and failure

• The mean and median

What is the expected value of a Bernoulli distribution if the probability of success is p?

• 0

• 1 - p

• p

• p^2

How is the variance of a Bernoulli distribution calculated?

• p^2 + (1 - p)^2

• p + (1 - p)

• p * (1 - p)

• p / (1 - p)

What is the variance of a Bernoulli distribution with p = 0.6?

• 0.36

• 0.24

• 0.16

• 0.06

In the example of an unfair coin, what is the probability of getting tails?

• 0.6

• 0.7

• 0.5

• 0.4

If an unfair coin lands on tails 60% of the time, what is the expected value when tails is assigned as 1?

• 0.6

• 0.5

• 0.7

• 0.4

What does the variance of 0.24 indicate in the unfair coin example?

• The probability of getting heads

• The likelihood of getting tails

• The average number of trials

• The spread of outcomes around the expected value