Intro starts week 2 pt1

What is the definition of probability?

Probability is the chance of something happening, taking a value between zero and one.

What does a probability of zero indicate?

A probability of zero indicates that there is no chance of an event occurring.

What is the range of values that probability can take?

Probability values range from 0 to 1.

How can you express probability as a percentage?

You can convert a probability by multiplying it by 100 to get a percentage.

What is the probability of getting heads in a coin toss?

The probability of getting heads in a coin toss is 0.5 (or 1/2).

What is the probability of rolling a four on a six-sided die?

The probability of rolling a four is 1/6.

What represents a random variable in probability notation?

A random variable is typically denoted by symbols like X, Y, or Z.

What does the notation P(X=x) represent?

It represents the probability that the random variable X takes the value x.

What are the two requirements for a valid probability distribution?

All probabilities must be between zero and one, and the sum of all probabilities must equal one.

What is a discrete probability distribution?

A distribution that gives probabilities for discrete outcomes, which are countable.

What are the two discrete probability distributions discussed in the lecture?

The Poisson distribution and the binomial distribution.

What does the Poisson distribution model?

It models the number of occurrences of a particular event over a fixed interval of time or space.

How is the mean of a Poisson distribution denoted?

It is denoted by the symbol λ (lambda).

What is the standard deviation of a Poisson distribution?

The standard deviation is the square root of the mean (λ).

What is the formula for calculating the mean of a discrete probability distribution?

The mean is calculated as the sum of all possible outcomes multiplied by their corresponding probabilities.

What does the symbol Σ (sigma) represent in probability calculations?

It represents the summation of a series of values.

In the context of this lecture, what does 'at least one' mean when calculating probabilities?

It means to consider all outcomes starting from one and above.

What is the complement rule in probability?

The complement rule states that the probability of an event occurring is 1 minus the probability of it not occurring.

What does a cumulative probability distribution table show?

It shows the accumulation of probabilities up to a certain value.

How do you determine the probability from a cumulative table?

You find the relevant mean in the row, then move down to the desired outcome in the column.

What happens in a context where the mean is provided in a question regarding Poisson distribution?

You use that information to find the corresponding probabilities from the Poisson tables.