Question

What are the requirements for a probability distribution? Differentiate between a discrete and a continuous random variable. Discuss the requirements for a binomial probability experiment.

Answer 1

Answer)

Requirements for a probability distribution are

1)

Sum of all the probabilities should be equal to 1

2)

Each and every probability should be in between 0 and 1

Discrete random variable takes only finite numbers

For example number of students in a class

There can be 50, 60, 70 or 64 students in a class

We cannot say that there are 64.75544 students

While continuous random variable can take any value in the interval

One example is height

Height can be 6.65488544 feet etc

Requirements for binomial distribution

Answer)

There should be fixed number of trials and probability of each and every trial should be same and independent of each other

Here we need to use the binomial formula

P(r) = ncr*(p^r)*(1-p)^n-r

Ncr = n!/(r!*(n-r)!)

N! = N*n-1*n-2*n-3*n-4*n-5........till 1

For example 5! = 5*4*3*2*1

Special case is 0! = 1

P = probability of single trial

N = number of trials

R = desired success