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

Answer:

a) Mean=1.2

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

Step-by-step 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

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

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• 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 $\sigma=\sqrt{X^2P(X)-(XP(X))^2}$

• Substitute the values i the formula we have
• $\sigma=\sqrt{10.86-(1.2)^2}$
• $=\sqrt{10.86-1.44}$
• $=\sqrt{9.42}$
• $=3.0692$

Therefore the standard deviation is  $\sigma=3.1$