Question

Consider the discrete probability distribution below. Complete parts a and b to the right.

Outcome Probability
0 0.35
1 0.36
2 0.14
3 0.08
4 0.04
5 0.02
6 0.01

a. Calculate the mean of this distribution.

μ = ? (Type an integer or a decimal.)

b. Calculate the standard deviation of this distribution.

σ = ? (Round to three decimal places as needed.)

Answer 1

a) Mean=1.2

b) The standard deviation is
`\sigma=3.1`

Explanation:

Given that the discrete probability distribution below :

Outcome Probability

0 0.35

1 0.36

2 0.14

3 0.08

4 0.04

5 0.02

6 0.01

a) To find the mean of this distribution :

The formula is
`E(X)=\sum X.P(X)`

X P(X) XP(X)
`X^2P(X)`

0 0.35 0 0

1 0.36 0.36 0.36

2 0.14 0.28 1.12

3 0.08 0.24 2.16

4 0.04 0.16 2.56

5 0.02 0.1 2.5

6 0.01 0.06 2.16

_________________________________________________

`\sum XP(X)=1.2`
`\sum X^2P(X)=10.86`

_________________________________________________

• Now substitute the value in the formula we get
• 
  `E(X)=\sum X.P(X)`
• 
  `E(X)=1.2`

Therefore Mean=1.2

b) To find Standard Deviation :

The formula is
`\sigma=√(X^2P(X)-(XP(X))^2)`

• Substitute the values i the formula we have
• 
  `\sigma=√(10.86-(1.2)^2)`
• 
  `=√(10.86-1.44)`
• 
  `=√(9.42)`
• 
  `=3.0692`

Therefore the standard deviation is
`\sigma=3.1`