x P(x)

0 0.2
1 0.3
2 0.2
3 0.3

Find the mean of this probability distribution. Round your answer to one decimal place.

To find the mean of a probability distribution, we need to multiply each value of x by its corresponding probability and then sum these products.

Let's calculate the mean step by step:

1. Multiply each value of x by its corresponding probability:
For x = 0: 0 * 0.2 = 0
For x = 1: 1 * 0.3 = 0.3
For x = 2: 2 * 0.2 = 0.4
For x = 3: 3 * 0.3 = 0.9

2. Sum these products:
0 + 0.3 + 0.4 + 0.9 = 1.6

3. Divide the sum by the total number of values:
Since there are 4 values in the probability distribution, we divide 1.6 by 4.

1.6 / 4 = 0.4

Therefore, rounding to one decimal place, the mean of this probability distribution is 0.4.