Compute the mean and variance of the following discrete probability distribution.
x P(x)
2 .50
8 .30
10 .20
Please assist and guide accordingly. Thank you so very much!
Here's a formula for the mean:
SUM[X * P(X)]
(Take each X times its respective P(X), then sum for a total. This will be your mean.)
Here's a formula for variance:
SUM[X^2 * P(X)] - mean^2
(Square each X. Take each X^2 times its respective P(X), then sum for a total. Subtract mean^2 from this value. This will be your variance.)
I hope this will help get you started.
To compute the mean and variance of a discrete probability distribution, you need to follow these steps:
Step 1: Multiply each value of x by its corresponding probability (P(x)).
- For example, for x = 2, its probability P(x) = 0.50. So, you multiply 2 * 0.50 = 1.
Step 2: Repeat this multiplication for each value of x and sum up the results.
- For x = 2, 2 * 0.50 = 1.
- For x = 8, 8 * 0.30 = 2.4.
- For x = 10, 10 * 0.20 = 2.
- Summing these results, 1 + 2.4 + 2 = 5.4.
Step 3: Compute the mean by dividing the sum from Step 2 by the total probability, which is 1.
- Mean = Sum / Total probability = 5.4 / 1 = 5.4.
Step 4: Compute the variance.
- To find the variance, you need to calculate the squared difference between each value of x and the mean and multiply it by the corresponding probability.
- For x = 2, (2 - 5.4)^2 * 0.50 = (-3.4)^2 * 0.50 = 11.56 * 0.50 = 5.78.
- For x = 8, (8 - 5.4)^2 * 0.30 = (2.6)^2 * 0.30 = 6.76 * 0.30 = 2.028.
- For x = 10, (10 - 5.4)^2 * 0.20 = (4.6)^2 * 0.20 = 21.16 * 0.20 = 4.232.
- Summing these results, 5.78 + 2.028 + 4.232 = 12.04.
Step 5: The variance is the sum from Step 4.
- Variance = 12.04.
So, the mean is 5.4 and the variance is 12.04 for the given discrete probability distribution.