Question

Consider the following data: x 4 5 6 7 8 P(X=x) 0.2 0.2 0.1 0.2 0.3...

Consider the following data:

x 4 5 6 7 8
P(X=x) 0.2 0.2 0.1 0.2 0.3

Copy Data

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≤8). Round your answer to one decimal place.

Step 5 of 5:

Find the value of P(X>4). Round your answer to one decimal place.

Homework Answers

Answer #1

Solution :

x P(x) x * P(x) x2 * P(x)
4 0.2 0.8 3.2
5 0.2 1 5
6 0.1 0.6 3.6
7 0.2 1.4 9.8
8 0.3 2.4 19.2
Sum 1 6.2 40.8

From given probability distribution,

1)

Mean = = X * P(X)

E(X) =   = 6.2

(2)

Variance = 2

= X 2 * P(X) - 2

V(X) = 40.8 - 6.22

= 2.36

(3)

standard deviation = 1.5

4)

P(X 8) = 1.0

(5)

P(X > 4) = 1 - P(X 4) = 1 - 0.2 = 0.8

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