Geometric Distribution Expected Value

Introduction to geometric probability distribution expected value:

The geometric probability distribution is one method in statistics. The probability of possible is determined by this method and it is giving the result between 0 to 1.The expected value is in geometric probability distribution is reciprocal of the success probability. Now we are going to see about geometric probability distribution expected value. I like to share this What is Geometric Mean with you all through my article.

Explanation for Geometric Probability Distribution Expected Value

Expected value of geometric probability distribution:

The expected value is differed based on probability distribution. In geometric probability distribution, the expected value is based on probability of success. The expected value means whole probability of success.

Expected value formula in geometric probability distribution:

The expected value in single success is E(X) = `1/p` .
The expected value in geometric probability is E(X) = Σx .P(X).

more about Geometric Probability Distribution Expected Value

Example problems for geometric probability distribution expected value:

Problem 1: Find out the expected value from the probability of success p =` 3/36` .

Solution:

The given probability of success is p = `3/36` =` 1/12` .

The formula for geometric probability distribution expected value is E(X) = `1/p` .

E(X) =` 1/(1/12)` = 12.

Therefore, the expected value of geometric probability distribution is 12.

Problem 2: Find out the expected value from probabilities of getting less than 6 in dice throw.

Solution:

The probability of getting less than 6 is

x     :  1    2   3   4   5

P(x):   `1/6`   ` 1/6`   `1/6`   `1/6`   `1/6`

The expected value of geometric distribution is E(X) = Σx .P(X)  .

E(X) = 1 x `1/6` + 2 x `1/6` + 3 x `1/6` + 4 x `1/6` + 5 x `1/6` = `1/6` + `2/6` + `3/6` + `4/6` + `5/6` = `(1 + 2+ 3+ 4+ 5)/6` = `15/6` .

Therefore, the expected value of geometric distribution is `15/6` .

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Exercise problems for geometric probability distribution expected value:

1. Find out the expected value from probability of success p = `2/3` .

Solution: Expected value of geometric probability distribution is E(X) = `3/2` .

2. Find out the expected value from probability of getting 3 or 4 in dice throw.

Solution: Expected value of geometric probability distribution is E(X) = `1/3` .