Discrete Probability Function or Not Examples

In this class, We discuss Discrete Probability Function or Not Examples.

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The reader should have prior knowledge of the Probability mass function. Click Here.

Discrete probability function or Probability mass function

The function should satisfy the two conditions.

1) f(x) >= 0 for each real number x.

2) Σall x f(x) = 1

Example 1:

Check the following functions serve as probability mass function.

f(x) = (x -2)/2 for x = 1,2,3,4

Solution: can not be served.

f(1) is negative

Example 2:

h(x) = x^2/2 for x = 0, 1, 2, 3, 4

solution: can not be served.

The Sum of all five probabilities is 6/5.

Example 3:

A random variable X has the following probability distribution.

The below table shows the probability distribution.

Find k?

Solution:

Σall x f(x) = 1

0 + k + 2k + 2k + 3k + k^2 + 7k^2 + k = 1

9k + 8k^2 = 1

k = (-9 +- √81+32)/16

k = 0.102