Question

Consider the following data:

x 4 5 6 7 8

P(X=x) 0.1 0.3 0.1 0.2 0.3

Step 1 of 5: Find the expected value E(X). Round your answer to one decimal place.

Step 2 of 5:

Find the variance. Round your answer to one decimal place.

Step 3 of 5:

Find the standard deviation. Round your answer to one decimal place.

Step 4 of 5:

Find the value of P(X>6)P(X>6). Round your answer to one decimal place.

Step 5 of 5:

Find the value of P(X≥8)P(X≥8). Round your answer to one decimal place.

Answer 1

Solution:

We have to find the expected value E(X),  the variance and the standard deviation of X.

Formula:

Mean or the expected value E(X):

Variance:

where

and

thus

x	P(x)	x*P(x)	x^2 *P(x)
4	0.1	0.4	1.6
5	0.3	1.5	7.5
6	0.1	0.6	3.6
7	0.2	1.4	9.8
8	0.3	2.4	19.2

Thus

Step 1 of 5: Find the expected value E(X).

Step 2 of 5: Find the variance.

where

thus

Step 3 of 5: Find the standard deviation.

Step 4 of 5: Find the value of P(X>6)

P(X>6) = P( X = 7) +P(X = 8)

P(X>6) = 0.2 + 0.3

P(X>6) = 0.5

Step 5 of 5: Find the value of P(X≥8)

P(X≥8) = P( X= 8)

P(X≥8) = 0.3