Salman Khan Β· @salkhanacademy. New personal twitter account for me that is separate from the Khan Academy account. Mountain View, CA. khanacademy.βorg.

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Jan 3, - Monte Carlo Simulation to Answer LeBron's Question. Simulation to Answer LeBron's Question Monte Carlo, Basketball Stats, Khan Academy.

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In finance, the Monte Carlo method is used to simulate the various sources of uncertainty that affect the value of the.

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Jan 3, - Monte Carlo Simulation to Answer LeBron's Question. Simulation to Answer LeBron's Question Monte Carlo, Basketball Stats, Khan Academy.

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Jan 3, - Monte Carlo Simulation to Answer LeBron's Question. Simulation to Answer LeBron's Question Monte Carlo, Basketball Stats, Khan Academy.

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Monte Carlo simulation (also known as the Monte Carlo Method) lets you see all the possible outcomes of your decisions and assess the impact of risk, allowing.

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been examined by utilizing Monte Carlo Simulation, to analyze the probability to Retrieved from Khan Academy: bestcarbest.ru

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Monte Carlo simulation (also known as the Monte Carlo Method) lets you see all the possible outcomes of your decisions and assess the impact of risk, allowing.

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Khan Academy, Mountain View nian Monte Carlo (HMC) (Duane et al., ; Neal, ). windowed acceptance method rely on detailed balance to.

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been examined by utilizing Monte Carlo Simulation, to analyze the probability to Retrieved from Khan Academy: bestcarbest.ru

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Instead, we repeat the experiment a large enough number of times to make the results practically equivalent to repeating forever. We can use table to see the distribution:. All of the other chapters in this part build upon probability theory. This rule is intuitive: think of a Venn diagram. Probability theory is useful in many other contexts and, in particular, in areas that depend on data affected by chance in some way. However, the sample function can be used directly, without the use of replicate , to repeat the same experiment of picking 1 out of the 5 beads, continually, under the same conditions. But to multiply like this we need to assume independence! Before delving into more complex examples, we use simple ones to demonstrate the computing tools available in R. To illustrate how we use these formulas and concepts in practice, we will use several examples related to card games. To do this, we take the number and suit of a card and create the card name like this:. Of course not. To do this, we sample with replacement : return the bead back to the urn after selecting it. For example, in poker, we can compute the probability of winning a hand based on the cards on the table. For more complicated cases, the computations are not as straightforward. In our very first example, we imagined an urn with five beads. Also, casinos rely on probability theory to develop games that almost certainly guarantee a profit. An example is the sample function in R. For example, if I have 2 red beads and 3 blue beads inside an urn 47 most probability books use this archaic term, so we do too and I pick one at random, what is the probability of picking a red one? Notice what happens when we ask to randomly select five beads:. As a reminder, to compute the probability distribution of one draw, we simply listed out all the possibilities. First, we use the function rep to generate the urn:. Here we focus on categorical data. To perform our first Monte Carlo simulation, we use the replicate function, which permits us to repeat the same task any number of times. Many examples of events that are not independent come from card games. It will help us understand the probability theory we will later introduce for numeric and continuous data, which is much more common in data science applications. If we know the relative frequency of the different categories, defining a distribution for categorical outcomes is relatively straightforward. In data science applications, we will often deal with continuous variables. This is an example of a Monte Carlo simulation. A popular way to pick the seed is the year - month - day. Computers provide a way to actually perform the simple random experiment described above: pick a bead at random from a bag that contains three blue beads and two red ones. But if I show you the result of the last four outcomes:. We can use induction to expand for more events:. This is actually fine since the results are random and change from time to time. In fact, this can be considered the mathematical definition of independence. We use paste to create strings by joining smaller strings. The function expand.{/INSERTKEYS}{/PARAGRAPH} We already saw an example of a conditional probability: we computed the probability that a second dealt card is a King given that the first was a King. Face cards are worth 10 points and Aces are worth 11 or 1 you choose. The events are not independent, so the probabilities change. The goal is to get closer to 21 than the dealer, without going over. Here we focus on how to use R code to compute the answers. As an example, imagine a court case in which the suspect was described as having a mustache and a beard. In probability, we use the following notation:. The classic example is coin tosses. Above we set it to We want to avoid using the same seed everytime. If we simply add the probabilities, we count the intersection twice so we need to substract one instance. In the exercises, we may ask you to set the seed to assure that the results you obtain are exactly what we expect them to be. We want to repeat this experiment an infinite number of times, but it is impossible to repeat forever. We will see more of these examples later. Error in sample. {PARAGRAPH}{INSERTKEYS}In games of chance, probability has a very intuitive definition. Not surprisingly, we get results very similar to those previously obtained with replicate. When events are not independent, conditional probabilities are useful. After you see what you have, you can ask for more. The probability distribution is:. In Blackjack, you are assigned two random cards. To see an extreme case of non-independent events, consider our example of drawing five beads at random without replacement:. In cases that can be thought of as beads in an urn, for each bead type, their proportion defines the distribution. This results in rearrangements that always have three blue and two red beads. We say two events are independent if the outcome of one does not affect the other. Answering questions about probability is often hard, if not impossible. A more tangible way to think about the probability of an event is as the proportion of times the event occurs when we repeat the experiment an infinite number of times, independently, and under the same conditions. We start by covering some basic principles related to categorical data. For instance, we know what it means that the chance of a pair of dice coming up seven is 1 in 6. The same is true when we pick beads from an urn with replacement. Random number generators permit us to mimic the process of picking at random. In a discrete probability course you learn theory on how to make these computations. As a result, Probability Theory was born. However, this is not the case in other contexts. We can now see if our definition actually is in agreement with this Monte Carlo simulation approximation. Discrete probability is more useful in card games and therefore we use these as examples. Because knowing how to compute probabilities gives you an edge in games of chance, throughout history many smart individuals, including famous mathematicians such as Cardano, Fermat, and Pascal, spent time and energy thinking through the math of these games. We use the very general term event to refer to things that can happen when something occurs by chance. Although this is a simple and not very useful example, we will use Monte Carlo simulations to estimate probabilities in cases in which it is harder to compute the exact ones. One of the goals of this part of the book is to help us understand how probability is useful to understand and describe real-world events when performing data analysis. We simply assign a probability to each category. This implies that many of the results presented can actually change by chance, which then suggests that a frozen version of the book may show a different result than what you obtain when you try to code as shown in the book. If we ask that six beads be selected, we get an error:. We demonstrate its use in the code below. For this, we will use the expand. The word probability is used in everyday language. Since each of the five outcomes has the same chance of occurring, we conclude that the probability is. Knowledge of probability is therefore indispensable for data science. Here we discuss a mathematical definition of probability that does permit us to give precise answers to certain questions. In the example above, the probability of red is 0. There were 5 and so then, for each event, we counted how many of these possibilities were associated with the event. The subset of probability is referred to as discrete probability. The function sample has an argument that permits us to pick more than one element from the urn. Say the conditional probability of a man having a mustache conditional on him having a beard is. The multiplication rule also applies to more than two events. Probability continues to be highly useful in modern games of chance. Today probability theory is being used much more broadly with the word probability commonly used in everyday language. However, by default, this selection occurs without replacement : after a bead is selected, it is not put back in the bag. The numbers above are the estimated probabilities provided by this Monte Carlo simulation. Throughout this book, we use random number generators. This line of code produces one random outcome. These events are therefore not independent : the first outcome affected the next one. Now you know that the probability of red is 1 since the only bead left is red.