. Find the mean and standard deviation of the following probability distribution:
x 1 2 3
P(x) 0.4 0.25 0.35
Please show all of your work.
To find the mean:
SUM [x * P(x)]
Multiply each x by its respective probability P(x). Add together for a total. This will be your mean.
To find variance:
SUM [x^2 * P(x)] - mean^2
Square each x. Multiply each squared x by its respective probability P(x). Add together for a total. Square the mean. Subtract the squared mean from the total. This will be your variance.
To find standard deviation:
Take the square root of the variance.
Hopefully, this information will help you with problems of this type.
To find the mean and standard deviation of a probability distribution, follow these steps:
Step 1: Multiply each value of x by its corresponding probability P(x).
x * P(x):
1 * 0.4 = 0.4
2 * 0.25 = 0.5
3 * 0.35 = 1.05
Step 2: Sum up the values obtained in Step 1.
0.4 + 0.5 + 1.05 = 1.95
Step 3: The sum obtained in Step 2 is the mean of the probability distribution.
Mean = 1.95
Step 4: Subtract the mean (1.95) from each value of x, square the result, and multiply by the corresponding probability P(x).
(x - Mean)^2 * P(x):
(1 - 1.95)^2 * 0.4 = 0.372
(2 - 1.95)^2 * 0.25 = 0.00125
(3 - 1.95)^2 * 0.35 = 0.83975
Step 5: Sum up the values obtained in Step 4.
0.372 + 0.00125 + 0.83975 = 1.213
Step 6: Take the square root of the sum obtained in Step 5.
Standard Deviation = √1.213
Therefore, the mean of the probability distribution is 1.95 and the standard deviation is approximately 1.101.