We can do the same here and easily derive a formula for the mean of a binomial random variable, rather than using the definition. Remember back in Section 6.1, we talked about the mean of a random variable as an expected value. If we randomly sample 50 students, how many would we expect to have been successful?Īgain, it's fairly straightforward - 70% of 50 is 35, so we'd expect 35. In Example 5, we said that 70% of students are successful in the Statistics course. We could do the same with any binomial random variable.
A binomial distribution has 100 trials free#
If she takes 100 free throws, how many would we expect her to make? (Remember that she historically makes 85% of her free throws.) Let's consider the basketball player again. Using that concept to find all the probabilities, we get the following distribution: Not only that, since the questions are independent, we can just multiply the probability of getting each one correct or incorrect, so P( ) = (3/4) 3(1/4).
In fact, we can use combinations to figure out how many ways there are! Since P(X=3) is the same regardless of which 3 we get correct, we can just multiply the probability of one line by 4, since there are 4 ways to get 3 correct. First, notice that there are multiple ways to get 1, 2, or 3 questions correct. So how can we find probabilities? Let's look at a tree diagram of the situation:įinding the probability distribution of X involves a couple key concepts. the probability of being correct is constant, since we're guessing: 1/4.each question has two outcomes - we're right or wrong.the questions are independent, since we're just guessing.
A binomial distribution has 100 trials how to#
Once we determine that a random variable is a binomial random variable, the next question we might have would be how to calculate probabilities.
Yes! There are fixed number of trials (ten rolls), each roll is independent of the others, there are only two outcomes (either it's a 6 or it isn't), and the probability of rolling a 6 is constant.
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