Probability Models by David Spade, PhD

About the Lecture

The lecture Probability Models by David Spade, PhD is from the course Statistics Part 1. It contains the following chapters:

Probability Models
The 10% Rule
The Binomial Model
Using the Normal Approximation
Statistical Significance

Included Quiz Questions

What is a significant problem in describing a discrete random variable with a continuous model?

Normal approximation does not allow us to find the probability of a particular number.
Normal approximation does not allow us to find the probability of a series of numbers.
Normal approximation does not allow us to find the probability of a particular range of dates.
Outliers prevent us from finding a discrete result.
Variance prevents us from finding a discrete result.

Suppose we are flipping a coin that comes up heads 40% of the time. What is the probability that the first flip of heads happens on the fourth trial?

The probability that the first head is on the fourth flip is 0.0864.
The probability that the first head is on the fourth flip is 0.4293.
The probability that the first head is on the fourth flip is 0.6425.
The probability that the first head is on the fourth flip is 0.
The probability that the first head is on the fourth flip is 0.5.

Suppose we are flipping a coin that comes up heads 40% of the time. What is the probability that heads comes up exactly twice?

The probability of getting 2 heads in 10 flips is 0.12.
The probability of getting 2 heads in 10 flips is 0.0027.
The probability of getting 2 heads in 10 flips is 0.20.
The probability of getting 2 heads in 10 flips is 0.
The probability of getting 2 heads in 10 flips is 0.25.

Suppose we are flipping a coin that comes up heads 40% of the time. Using the normal approximation, what is the probability that heads comes up between 30 and 45 times after 100 flips?

The probability that the number of heads is between 30 and 45 is 0.83.
The probability that the number of heads is between 30 and 45 is 0.32.
The probability that the number of heads is between 30 and 45 is 1.0
The probability that the number of heads is between 30 and 45 is 0.26.
The probability that the number of heads is between 30 and 45 is 0.15.

What is NOT true of the normal approximation to the binomial model?

The normal approximation can be used to find the probability that we see a particular number or a range of numbers of successes.
In order to use the normal approximation, we need to have the expected number of successes and the expected number of failures each exceed 10.
In order to use the normal approximation to the binomial model, the conditions of the binomial model must be satisfied.
A problem with the normal approximation comes from trying to approximate the distribution of a discrete random variable using a continuous distribution.
We may use this approximation when the success/failure condition is satisfied.

If the probability of success is 0.2 and X is the random variable corresponding to the trial on which the first success occurs then what is E(X)?

If the probability of success is 0.2 and X is the random variable corresponding to the trial on which the first success occurs then what is SD(X)?

What is the value of 5!?

What is the value of E(Y) under binomial distribution if n = 2 and p = 0.5?

What is the value of SD(Y) under binomial distribution if n = 2 and p = 0.5?