The following table contains the probability distribution for X = the number of retransmissions necessary to successfully transmit a 1024K data package through a double satellite media.
X
0
1
2
3
P(X)
0.35
0.25
***
0.15
The variance for the number of retransmissions is?
1.79
2.19
1.6
1.16
To find the variance, we first need to calculate the mean of the distribution:
Mean (µ) = Σ [X * P(X)]
Mean (µ) = (0 * 0.35) + (1* 0.25) + (2 * ?) + (3 * 0.15)
Mean (µ) = 0 + 0.25 + 0 + 0.45
Mean (µ) = 0.7
Now we can calculate the variance using the formula:
Variance = Σ [ (X - µ)^2 * P(X) ]
Variance = (0 - 0.7)^2 * 0.35 + (1 - 0.7)^2 * 0.25 + (2 - 0.7)^2 * ? + (3 - 0.7)^2 * 0.15
Variance = 0.49 * 0.35 + 0.09 * 0.25 + ? + 2.89 * 0.15
Variance = 0.1715 + 0.0225 + ? + 0.4335
Variance = 0.6275 + ?
We know that the sum of all probabilities equals 1, so:
0.35 + 0.25 + ? + 0.15 = 1
0.75 + ? = 1
? = 0.25
Therefore, the variance is:
Variance = 0.6275 + 0.25
Variance = 0.8775
So, the variance for the number of retransmissions is 0.8775.