In fact, P(num heads = 0) in 10 tosses is. This would be very surprising because the probability of that happening is very small. Next, suppose that the number of heads is “0”. Imagine that you toss a coin 10 times in a row and count the number of heads. What does this table tell us and where did the numbers come from? Given this, we can create a TABLE OF PROBABILITIES Each toss is independent because its result is not affected by the toss before or after it. However, we are tossing 10 times and counting the number of heads. Therefore, for each individual toss, P(head) =. 5) chance or getting a head and a 50% (or. We know that when using a fair coin, we have a 50% (or. There are no other possible values that can result from this experiment. Remember that the experiment is tossing a coin 10 times and counting the number of heads. The sample space is a collection of all possible outcomes of the experiment. What is the sample space in this example? THINK ABOUT THIS: What do you think this distribution would look like? In other words, if you repeated this 1000 times recorded the number of heads each time, what would you expect? However, those data values can only be 0, 1, 2, 3, 4, 5, 6, 7, 8, 9 or 10. If you repeat this say 1000 times, you will have 1000 data values for this experiment. Then again, you toss the coin 10 times and record the number heads. In other words, you toss the coin 10 times and record the number of heads. ![]() To create a “distribution” for this experiment, you would repeat the experiment over and over. The “result” is the number of heads you get. NOTE: Tossing the coin 10 times (in this example) is the “experiment”. It is a variable because the value of X will vary or change each time you toss the coin 10 times. It is discrete because the only possible number of heads you can get are 0, 1, 2, 3, 4, 5, 6, 7, 8, 9 or 10. However, there is no way to predict how many you will get – it is random. It is random, because you can get 0, 1, 2, 3, 4, 5, 6, 7, 8, 9 or 10 heads total each time you toss the coin 10 times. In this case, “X” represents a “random discrete variable”. In addition, because the number of heads you will get each time you toss the coin 10 times can be different, you can let X be the number of heads you get when you toss the coin 10 times. However, if you continue to toss the coin 10 times, count the number of heads each time, and writing down that number, you will be collecting “data” that follows the “ binomial distribution”. Suppose you toss a coin over and over again and each time you can count the number of “Heads” you get.įor example, if you decide to toss the coin 10 times, and you get 4 Heads and 6 Tails, then in that case, the number of heads is 4. This Tutorial will explain the Binomial Distribution, Formula, and related Discrete Probabilities
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