in a jar. Number of telephone calls at a particular time. Number of cars sold by a car dealer in one month, etc., For instance, three responsible persons say, P , P and P are asked about their opinion in favour of building a model school in a certain district. Each person’s response is recorded as Yes (Y) or No (N).
Determine the random variable that could be of interest in this regard. The possibilities of the response are as follows Table . Possibilities P P P Values of Random variable (Number of Yes those who are given) . Y Y Y .
Y Y N . Y N Y . Y N N . N Y Y .
N Y N . N N Y . N N N Form the above table, the discrete random variable take values , , and . Probability Mass function Definition .
If X is a discrete random variable with distinct values x x n , ..., , ... , then the function, denoted by P X ( ) and defined by p x if x x i if x i i i i , ,..., ,... ≠ p(x)= P(X=x i This is defined to be the probability mass function or discrete probability function of X . The probability mass function p x ( ) must satisfy the following conditions (i) p x i i ≥∀ (ii) p x i i ) = ∞ Example .
The number of cars in a household is given below. No. of cars No. of Household Estimate the probability mass function.
Verify p x i ) is a probability mass function. Let X be the number of cars XII Std - Business Maths & Stat EM Chapter - - Random Variable and Mathematical Expectation Table . x i Number of Household p x i . .