SaiBook.us Statistics

Lesson Example Discussion Quiz: Class Homework

Example

Title: Geometric distribution

Grade: 9-a Lesson: S4-L6

Explanation: The best way to understand statistics is by looking at some examples. Take turns and read each example for easy understanding.

Examples:

Suppose you are playing a game of darts. The probability of success is 0.4. What is the probability that you will hit the bullseye on the third try and find its mean and variance?

Step 1a

Identify p,x

Explanation:

Probability of success p = 0.4

1-p = 1-0.4

1-p = 0.6

x = 3

Step 1b

Calculate Probability P(x)

Explanation:

P(X=x)=\$(1-p)^(x-1) × p\$

P(X=3) = \$(1-0.4)^(3-1) × 0.4\$

P(X=3) = \$(0.6)^(2) × 0.4\$

P(X=3) = \$0.36 × 0.4\$

The probability that you will hit the bullseye on the third try is 0.144.

Step 1c

Calculate mean \$\mu\$ and variance \$\sigma^2\$

Explanation:

Mean \$\mu = 1/p = 1/0.4\$

Mean \$\mu\$ = 2.5

Variance \$\sigma^2 = (1-p)/p^2 = (1-0.4)/0.4^2\$

\$\sigma^2 = 0.6/0.16\$

Variance \$\sigma^2\$ = 3.275