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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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7
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Mitch S
please write clearer. Thank you for this lesson.
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Andy S
How do you find out the probability of achieving specific numbers with multiple dice, say the outcome that you would roll exactly 3 fives out of 5 dice or at least 3 fives out of 5 dice
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Andy S
*or at least 1 five out of 5 dice
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Mark Huber
Let's do exactly 3 fives out of 5 dice. A sequence of five dice rolls could be of the form 5N55N, where N stands for any number other than 5. There are other forms that have exactly three 5's: N555N, 5NN55, and so on. The number of such forms is what mathematicians call 5 choose 3, and the formula for finding them is 5!/(3!(5-2)!), where the ! is the factorial operator. 5! = 5*4*3*2*1 = 120, 3! = 3*2*1 = 6, and (5-3)! = 2! = 2*1 = 2. So 5 choose 3 is 120/(6*2) = 120/12 = 10. (continued)
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Mark Huber
Okay, so there are 10 forms. What is the chance of a particular form, say 555NN? The first five has chance 1/6, the second five 1/6, the third five 1/6, the fourth N 5/6 (remember it is any number that is not a 5), the fifth N 5/6. So overall there is a (1/6)(1/6)(1/6)(5/6)(5/6) = 5^2/6^5 chance of that form. There are 10 forms, so the overall chance is 10*5^2/6^5 = 125/3888 or approximately 0.03215...
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Leyla S
Perfectly presented, thank you very much!
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Mark Huber
Thanks, Leyla!
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