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Introduction to Probability & Statistics
67 CQ
10 Lessons
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7 CQ
In this lesson, discover the building blocks of probability, including random variables, set notation, and two important rules for calculating probabilities.
with Mark HuberIn this lesson, discover the building blocks of probability, including random variables, set notation, and two important rules for calculating probabilities.
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7 CQ
There are two main types of random variables: discrete and continuous. In this lesson on foundational concepts in statistics and probability, see how they work!
with Mark HuberThere are two main types of random variables: discrete and continuous. In this lesson on foundational concepts in statistics and probability, see how they work!
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6 CQ
Discover the Strong Law of Large Numbers, discrete random variables, and learn how to calculate variance in this lesson on statistics and probability.
with Mark HuberDiscover the Strong Law of Large Numbers, discrete random variables, and learn how to calculate variance in this lesson on statistics and probability.
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8 CQ
Conditional probabilities add extra information to random variables. They're calculated using the conditional probability formula and Bayes' Rule, covered here.
with Mark HuberConditional probabilities add extra information to random variables. They're calculated using the conditional probability formula and Bayes' Rule, covered here.
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6 CQ
The Central Limit Theorem says that the sum of random variables tends to look like a normal distribution. Use this to approximate probabilities in this lesson!
with Mark HuberThe Central Limit Theorem says that the sum of random variables tends to look like a normal distribution. Use this to approximate probabilities in this lesson!
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Andy S
Could you further explain your continuous r.v. dice example. I'm confused by what the value of x is in that example and why it could never be achieved
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Mark Huber
Let's do an example. What is the probability that X = 1/3? Well, 1/3 is in the left half of the interval from 0 to 1 (write [0,1] for the whole interval, and [0,1/2] for the left half.) So the first die roll must be even in order for X to even have a chance of equaling 1/3.
Suppose the first die roll was even, so now we are in the left half [0,1/2]. The number 1/3 is in the right half of that interval (in [1/4,1/2]) so we would have to roll odd at the next die roll...
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Mark Huber
...which puts X in [1/4,3/8]. But then 1/3 is in the left half of [1/4,3/8] so we'd half to roll left again.
In fact, we would have to roll even, odd, even, odd, even, odd, .... forever to get X = 1/3. The chance that we roll that exact sequence is (1/2)*(1/2)*(1/2)*... = 0. In fact, no matter what little x I pick in [0,1], the chance that X exactly hits the value will be 0.
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