Introduction to Probability and Probability Distributions
Probability Distributions
Random Variables
Random variables are the variables that can make many numbers.
With the coin example, $X$ can take either 1 or 0, not just a single number.
Which of the following are examples of discrete random variables? Select all that apply.
- Selecting a card from a deck
- Drawing a marble from a bag of colored marbles
- Measuring the temperature in degrees Fahrenheit
- Counting the number of cars passing through a toll booth
Answer
1, 2, 4
Since the possible outcomes are countable and distinct, it qualifies as an example of a discrete random variable.
Probability Distributions (Discrete)
Binomial Distribution
A binomial distribution is a histogram of probabilities.
It is an example of discrete distributions.
The distribution is symmetrical if the probability is equal and is skewed if it's not equal.
What is the probability of getting three ones when rolling a dice five times (no matter which dice)?
${5 \choose 3}({1\over6})^3({5\over6})^2$
If X is the number of times we get a 1 when rolling a dice ten times, then $X \sim \operatorname{Binomial}(n, p)$, where n, p is equal to:
n = 10, p = 1/6
Correct. The probability of getting a 1 when throwing one dice is 1/6. And n is the total of experiments (10 times).
Binomial Coefficient
The binomial coefficient is a way to obtain k elements out of a set of n in an unordered way.
Bernoulli Distribution
Bernoulli distribution is a distribution of successful cases.
Throwing a 4-sided fair dice and observing if it lands in 2 or not might be modeled as a Bernoulli distribution with p equal to:
1/4
Correct! In a 4-sided fair dice, there is a 1/4 probability of landing in each face.
All the information provided is based on the Probability & Statistics for Machine Learning & Data Science | Coursera from DeepLearning.AI
