I am to find the mean, variance, and standard deviation for the probability distribution. I don't even know where to start. Here is the problem
x P(x)
0 0.19
1 0.32
2 0.28
3 0.21
In google type:
wikipedia mean variance standard deviation
When you see list of results click on pages in list.
Then in google type:
mathisfun Standard Deviation Calculator
When you see list of results click on:
mathsisfuncom/data/standard-deviation-calculator.html
When page be open type your numbers and click ENTER button on your keyboard. You will see result.
This is not right. I know how to find the mean, variance, and standard deviation normally. This problem is for probability distribution, which is an entirely different formula.
To find the mean, variance, and standard deviation for this probability distribution, you can follow these steps:
Step 1: Calculate the expected value (mean).
The expected value or mean (μ) is calculated by multiplying each value by its corresponding probability and summing them up.
μ = (0 x 0.19) + (1 x 0.32) + (2 x 0.28) + (3 x 0.21)
Step 2: Calculate the variance.
The variance (σ^2) is calculated by taking each value subtracted by the mean, squaring the result, multiplying it by the corresponding probability, and summing them up.
σ^2 = [(0 - μ)^2 x 0.19] + [(1 - μ)^2 x 0.32] + [(2 - μ)^2 x 0.28] + [(3 - μ)^2 x 0.21]
Step 3: Calculate the standard deviation.
The standard deviation (σ) is the square root of the variance.
σ = √σ^2
Now, let's calculate each step:
Step 1:
μ = (0 x 0.19) + (1 x 0.32) + (2 x 0.28) + (3 x 0.21)
μ = (0) + (0.32) + (0.56) + (0.63)
μ = 1.51
Step 2:
σ^2 = [(0 - μ)^2 x 0.19] + [(1 - μ)^2 x 0.32] + [(2 - μ)^2 x 0.28] + [(3 - μ)^2 x 0.21]
σ^2 = [(0 - 1.51)^2 x 0.19] + [(1 - 1.51)^2 x 0.32] + [(2 - 1.51)^2 x 0.28] + [(3 - 1.51)^2 x 0.21]
σ^2 = [2.2801 x 0.19] + [0.2601 x 0.32] + [0.2369 x 0.28] + [2.2801 x 0.21]
σ^2 = 0.4338 + 0.0832 + 0.0662 + 0.4788
σ^2 = 1.0619
Step 3:
σ = √σ^2
σ = √1.0619
σ ≈ 1.030
So, the mean (μ) is 1.51, the variance (σ^2) is 1.0619, and the standard deviation (σ) is approximately 1.030.
To find the mean, variance, and standard deviation for the probability distribution, you need to follow a few steps:
1. Calculate the mean:
- Multiply each value of x by its corresponding probability P(x).
- Sum up these values.
2. Calculate the variance:
- Subtract the mean from each value of x and square the result.
- Multiply each squared result by its corresponding probability P(x).
- Sum up these values.
3. Calculate the standard deviation:
- Take the square root of the variance calculated in step 2.
Now, let's work through the problem together:
1. Calculate the mean:
- Multiply each value of x by its corresponding probability P(x):
0 * 0.19 = 0
1 * 0.32 = 0.32
2 * 0.28 = 0.56
3 * 0.21 = 0.63
- Sum up these values: 0 + 0.32 + 0.56 + 0.63 = 1.51
2. Calculate the variance:
- Subtract the mean from each value of x and square the result:
(0 - 1.51)^2 = 2.2801
(1 - 1.51)^2 = 0.2601
(2 - 1.51)^2 = 0.2401
(3 - 1.51)^2 = 2.2801
- Multiply each squared result by its corresponding probability P(x):
2.2801 * 0.19 = 0.433419
0.2601 * 0.32 = 0.083232
0.2401 * 0.28 = 0.067228
2.2801 * 0.21 = 0.479721
- Sum up these values: 0.433419 + 0.083232 + 0.067228 + 0.479721 = 1.0636
3. Calculate the standard deviation:
- Take the square root of the variance calculated in step 2:
√1.0636 ≈ 1.031
After performing these calculations, the mean is 1.51, the variance is 1.0636, and the standard deviation is approximately 1.031.