- Consider a fixed number of n of Bernoulli trials with probability of success p in each trial. Each trial can result in just two possible outcomes. We call one of these outcomes a success and the other, a failure.
- The number of successes in n trials is a random variable (X). The probability distribution of X is known as a binomial distribution.
1.1. Binomial Distribution in R-Programming
- Poisson Distribution formula
- P(x= a) = dbinom
- P(x<=a) = pbinom
- P(x>a) = 1 - P(x<= a - 1) = 1 - pbinom(a-1)
- According to the Mendelian theory of inheritance, a cross fertilization of related species of red and white flowered plants produces offsprings of which 25%are red flowered plants. Suppose that a horticulturist wishes to cross 5 pairs of red and white flowered plants. Of the 5 offsprings, what is the probability that:
- There will be no red flowered plants?
- P(x=0) = dbinom(0, 5, 0.25) = 0.2373047
- There will be 4 or more red flowered plants?
- P(x>4) = 1- P(x <= a -1) = 1 - pbinom(3, 5, 0.25) = 0.015625
- There will be either 2 or 3red flowered plants?
- P(x=2) + P(x=3) = dbinom(2, 5, 0.25) + dbinom(3, 5, 0.25) = 0.3515625