Question 1159943: The probability of x is given below
X P(x)
2 .10
4 .20
6 .30
8 .40
Answer the following questions
a) What is the probability that x is less than or equal to 4?
b) What is the probability that x is greater than or equal to 2?
c) Calculate the expected value
d) Calculate the variance
e) Calculate the standard deviation
Answer by jim_thompson5910(35256)   (Show Source):
You can put this solution on YOUR website!
Part a)
The answer is 0.3 since we add the P(x) values when x is 4 or smaller, so when x = 2 or x = 4.
0.10+0.20 = 0.30 = 0.3
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Part b)
"x is greater than or equal to 2" is basically saying "every x value mentioned in the table" because x = 2 is the smallest item listed.
Add up all the P(x) values. You should get 1 as the result. With any probability distribution, all the P(x) values must add to 1 to represent 100%.
Answer = 1
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Part c)
Make a column of the product of the X and P(X) values
| X | P(X) | X*P(X) | | 2 | 0.1 | 0.2 | | 4 | 0.2 | 0.8 | | 6 | 0.3 | 1.8 | | 8 | 0.4 | 3.2 |
Then add up the values in that new third column: 0.2+0.8+1.8+3.2 = 6
Expected value = 6
The expected value is another term for the mean.
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Part d)
Make yet another column. This time we'll represent the X^2*P(X) values
| X | P(X) | X*P(X) | X^2*P(X) | | 2 | 0.1 | 0.2 | 0.4 | | 4 | 0.2 | 0.8 | 3.2 | | 6 | 0.3 | 1.8 | 10.8 | | 8 | 0.4 | 3.2 | 25.6 |
Those new values add to: 0.4+3.2+10.8+25.6 = 40
Then we subtract off the square of the mean, or expected value, we got back in part c
40 - (mean)^2 = 40 - 6^2 = 40 - 36 = 4
The variance is 4
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Part e)
Apply the square root to the variance to get the standard deviation:
standard deviation = sqrt(variance)
standard deviation = sqrt(4)
standard deviation = 2
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