Sentences with BINOMIAL-DISTRIBUTION
Check out our example sentences below to help you understand the context.Sentences
1
"The binomial distribution is commonly used in statistics to model the number of successes in a fixed number of independent Bernoulli trials."
2
"The probability mass function of the binomial distribution is given by the formula P(X=k) = (n choose k) * p^k * (1-p)^(n-k), where X is the random variable representing the number of successes, n is the number of trials, and p is the probability of success in each trial."
3
"The binomial distribution is symmetric when the probability of success and failure is equal."
4
"The mean of a binomial distribution is given by the formula mean = n * p, where n is the number of trials and p is the probability of success in each trial."
5
"The variance of a binomial distribution is given by the formula variance = n * p * (1-p), where n is the number of trials and p is the probability of success in each trial."
6
"In a binomial distribution, the number of successes must be a non-negative integer and cannot exceed the number of trials."
7
"The binomial distribution is used to model various real-life scenarios such as coin flips, election outcomes, and defective product rates."
8
"The cumulative distribution function of the binomial distribution can be calculated using the formula P(X<=k) = Σ(i=0 to k) (n choose i) * p^i * (1-p)^(n-i), where X is the random variable representing the number of successes and k is a non-negative integer."
9
"The binomial distribution converges to the normal distribution when the number of trials is large and both the number of successes and failures are positive."
10
"The binomial distribution is a discrete probability distribution."
11
"The concept of the binomial distribution was first introduced by Jacob Bernoulli in the late 17th century."
12
"The skewness of a binomial distribution is typically negative if the probability of success is less than 0.5, indicating a left skew, and positive if the probability of success is greater than 0.5, indicating a right skew."
13
"The binomial coefficient in the binomial distribution formula represents the number of ways to choose k successes out of n trials."
14
"The binomial distribution can be used to calculate the probability of getting a specific number of successes in a given number of trials."
15
"The binomial distribution can be approximated by the Poisson distribution when the number of trials is large and the probability of success is small."
16
"The binomial distribution is widely used in hypothesis testing and statistical inference."
17
"In a binomial distribution with a fixed number of trials, as the probability of success increases, the distribution becomes more peaked."
18
"The binomial distribution is also used in quality control to determine the probability of having a certain number of defective items in a sample."
19
"The binomial distribution is an important concept in probability theory and has numerous applications in various fields."
1
"The binomial distribution is commonly used in statistics to model the number of successes in a fixed number of independent Bernoulli trials."
2
"In a binomial distribution, each trial must be independent and have the same probability of success."
3
"The mean and variance of a binomial distribution can be calculated using the formulas n*p and n*p*(1-p) respectively, where n is the number of trials and p is the probability of success."
4
"The binomial distribution is often used to analyze the outcomes of flipping a coin a certain number of times."
5
"The binomial distribution is useful for analyzing the probability of obtaining a specific number of defective products in a production line."
6
"In genetics, the binomial distribution can be used to model the probability of inheriting a certain gene from a parent."
7
"The binomial distribution is one of the most commonly studied probability distributions in statistics."
8
"The binomial distribution is characterized by a discrete probability function and a finite number of possible outcomes."
9
"The binomial distribution is symmetrical when the probability of success is equal to the probability of failure."
10
"The binomial distribution is often applied in hypothesis testing and decision-making processes in various fields."
