Answer :
The variance of X is 141. Therefore, the correct answer is: d. 141
To calculate the variance of a discrete random variable, you can use the following formula:
[tex]Var(X) = \sum_{x} (x - \mu)^2 \cdot P(x)[/tex]
Where:
- x represents each possible value of the random variable.
- μ is the mean (expected value) of the random variable.
- P(x) is the probability of the random variable taking the value x.
Given the probability distribution:
X | F(x)
------------
40 | 0.40
50 | 0.10
60 | 0.30
70 | 0.20
First, calculate the mean (expected value) of X:
μ = Σ [ x * P(x) ]
= (40 * 0.40) + (50 * 0.10) + (60 * 0.30) + (70 * 0.20)
= 16 + 5 + 18 + 14
= 53
Now, calculate the variance using the formula:
Var(X) = Σ [ (x - μ)² * P(x) ]
= ( (40 - 53)² * 0.40 ) + ( (50 - 53)² * 0.10 ) + ( (60 - 53)² * 0.30 ) + ( (70 - 53)² * 0.20 )
= (169 * 0.40) + (9 * 0.10) + (49 * 0.30) + (289 * 0.20)
= 67.6 + 0.9 + 14.7 + 57.8
= 141
So, the variance of X is 141. Therefore, the correct answer is: d. 141
Learn more about Variance here:
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