Discrete Probability Distributions

Discrete probability theory deals with the events that occur in the countable sample spaces.

Examples: The throwing dice, experiments with decks of the cards, and random walk.

Classical definition: Initially the probability of the event to occur was defined as number of cases favorable for the event, over the number of total outcomes possible in an equiprobable sample space.

Understanding Sample Space in Probability is always challenging for me but thanks to all math help websites to help me out.

For example if the event are occurrence of an even number when a die is rolled, the probability is given by 3/6=1/2 since 3 faces out of the 6 have even numbers and each face has the same probability  of appearing.

Definition

In probability theory is a probability distribution it is called discrete if it is characterized by a probability mass function. Thus the distribution of the random variable X is discrete and X is then called a discrete random variable,

If a random variable is discrete then the set of the all values that it can assume with non-zero probability is finite or countably infinite because the sum of uncountably many positive real numbers (which is the least upper bound of the set of all finite partial sums) always diverges to infinity.

Typically this is the set of possible values is a topologically discrete set in the sense that all its points are isolated points. But there are the discrete random variables for which this countable set is dense on the real line.

Among the most of well known discrete probability distributions are used for statistical modeling are the Poisson distribution, the Bernoulli distribution, the binomial distribution, the geometric distribution, and the negative binomial distribution. In the addition of the discrete uniform distribution is commonly used in computer programs that make equal probability random selections between a number of choices.

Example

The child psychologist is the interested in the number of times a newborn baby's crying wakes its mother after midnight. For the random sample of the 50 mothers the following information was obtained. Let X = the number of times newborn wakes its mother after midnight. For this example, x = 0, 1, 2, 3, 4, 5.

P(X = x) = Probability that X takes on a value x.

P(X = 0) = 2/50

P(X = 1) = 11/50

P(X = 2) = 23/50

P(X = 3) = 9/50

P(X = 4) = 4/50

P(X = 5) = 1/50
X values 0, 1, 2, 3, 4, 5.

My forthcoming post is on Dividing Mixed Number and cbse sample papers for class 10th will give you more understanding about Algebra.

The sum of probabilities is 1 that is

2/50+11/50+23/50+9/50+4/50+1/50=1