SOLUTION: x P(x) 0 0.1 1 0.15 2 0.15 3 0.6 Find the mean of this probability distribution. Round your answer to one decimal place. Find the standard deviation of this probabil

Algebra ->  Probability-and-statistics -> SOLUTION: x P(x) 0 0.1 1 0.15 2 0.15 3 0.6 Find the mean of this probability distribution. Round your answer to one decimal place. Find the standard deviation of this probabil      Log On


   

Question 1206814: x P(x)
0 0.1
1 0.15
2 0.15
3 0.6
Find the mean of this probability distribution. Round your answer to one decimal place.

Find the standard deviation of this probability distribution. Give your answer to 2 decimal places.


Found 2 solutions by MathLover1, math_tutor2020:
Answer by MathLover1(20850) About Me  (Show Source):
You can put this solution on YOUR website!

x|P%28x%29
0+|0.1
1| 0.15
2| 0.15
3|+0.6
Find the mean of this probability distribution. Round your answer to one decimal place
to find the mean (expectation) of the given distribution, we will use the following formula:
mu=sum%28x%2Ap%28x%29%29=0%2A0.1%2B1%2A0.15%2B2%2A0.15%2B3%2A0.6
mu=0%2B0.15%2B0.30%2B1.8
mu=2.25
mu=2.3


Find the standard deviation of this probability distribution. Give your answer to 2 decimal places.

sigma=sqrt%28sum%28x%5E2%2Ap%28x%29%29-mu%5E2%29

since mu=2.3, and
sum%28x%5E2%2Ap%28x%29%29=0%5E2%2A0.1%2B1%5E1%2A0.15%2B2%5E2%2A0.15%2B3%5E2%2A0.6=6.15
we have
sigma=sqrt%286.15-%282.3%29%5E2%29
sigma=sqrt%286.15-5.29%29
sigma=sqrt%280.86%29
sigma=0.9273618495495703
sigma=0.93


Answer by math_tutor2020(3817) About Me  (Show Source):
You can put this solution on YOUR website!

Answers:
mean = 2.3
standard deviation = 1.04

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Work Shown

xP(x)
00.1
10.15
20.15
30.6


Multiply the x and P(x) values to form a new column.
Spreadsheet software is recommended.
xP(x)x*P(x)
00.10
10.150.15
20.150.3
30.61.8

Add up the values in that new column to get the mean aka expected value.
The spreadsheet command called "SUM" is useful for adding up numbers quickly.
mu = 0 + 0.15 + 0.3 + 1.8 = 2.25
This rounds to 2.3 when rounding to one decimal place.

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mu = 2.25 = mean

Introduce a new column called (x-mu)^2*P(x)
The naming of this column should be self-explanatory. If not then please let me know.
xP(x)x*P(x)(x-mu)^2*P(x)
00.100.50625
10.150.150.234375
20.150.30.009375
30.61.80.3375

variance = sum of the (X-mu)^2*P(X) values
variance = 0.50625+0.234375+0.009375+0.3375
variance = 1.0875

Then,
SD = standard deviation
SD = sqrt( variance )
SD = sqrt( 1.0875 )
SD = 1.0428327 approximately
SD = 1.04 when rounding to 2 decimal places.

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Another way to find the variance is to introduce a column labeled x^2*P(x)
xP(x)x*P(x)x^2*P(x)
00.100
10.150.150.15
20.150.30.6
30.61.85.4

Adding up all of the x^2*P(x) values will get us
0 + 0.15 + 0.6 + 5.4 = 6.15
Subtract off mu^2 = (2.25)^2 = 5.0625 and you'll get:
6.15 - 5.0625 = 1.0875 which is the variance we calculated in the previous section above.


So there are two versions we could use
variance = Sum of (x-mu)^2*P(x) values
or
variance = [Sum of x^2*P(x) values] - mu^2