Question

Probability distribution of a random variable.

Answer 1

A tabular distribution gives the values of the random variable along with the corresponding probabilities is called its probability distribution. Let 10 families, whose number of families are respectively 3, 4, 3, 2, 5, 4, 3, 6, 4, 5. Thus random variable can accept any value from X, 2,3,4,5 and 6 which depends on which family is selected. Out of these 10 families, only one family is f₄ which has 2 members. Three families are such that f₁, f₃, f₅ each has 3 members. Three families are such that f₂, f₆, f₉ each has 4 members. Two families f₅ and f₁₀ are such that each has 5 members and only one family f₈ such that which has 6 members. Thus value of X will be only 2, if f₄ is selected. Since selection of each family is equally likely.

Thus probability that/4 is selected is \(\frac{1}{10}.\) Again, value of random variable X will be 3, if selected family is f₄ or f₃ or f₇. It means

P(X = 2) = \(\frac{1}{10},\) P(X = 3) = \(\frac{3}{10},\) P(X = 4) = \(\frac{3}{10},\)

P(X = 5) = \(\frac{2}{10}.\) P(X = 6) = \(\frac{1}{10}\)

Definition :

The probability distribution of random Variable X is system of following numbers:

Here, possible values of random variable X are real numbers x₁ x₂, x₃ ..., x_n and p_i (i = 1,2,..., n) is probability of acception xi by random variable X. It can be shown as: