Binomial distribution

Question 1

when a data set has a binomial distribution?

Answer 1

Binomial distribution is for discrete variables. lies the notion of a Bernoulli trial. A Bernoulli trial is a random experiment in which there are only two outcomes. It is customary to call these outcomes as Success and Failure. The probability of Success when we conduct the Bernoulli trial is p (0 < p < 1) and the probability of Failure is 1-p = q.

Question 2

counting techniques

how many ways can arrange these n objects in order?

Answer 2

n!

0! = 1.

Question 3

Permutations

Suppose we have N distinct objects. We want to select n of these objects and arrange them in order. In how many ways can this be done?

Answer 3

P^N_n=N!/(N−n)!

Question 4

Combinations

Suppose we have N distinct objects. We want to select n objects. In how many ways we can do the selection? The order these objects are arranged is immaterial.

Answer 4

(N)=N!/[n!∗(N−n)!]
(n)

Question 5

what is the diference between permutations and combinations?

Answer 5

Permutations are about how many different ordered sequences are possible
Combinations are about how many different unordered sets are possible

Question 6

Biniomial Distribution

Suppose we conduct the trial independently under identical conditions some n times. How many times will we get successes?

Answer 6

• Pr(0 successes)=P(0)=q^n=Pr(All failures)
• Pr(x successes from n)=P(x)=(n) p^x q^(n−x)
  (x)
• Pr(n successes)=P(n)=p^n=P(all successes)

(n_X) All these (n+1) probabilities must add up to one

(0 < p < 1) Failure is 1-p = q.