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
0.35
***
0.05
The standard deviation of the number of retransmissions is?
To calculate the standard deviation of the number of retransmissions, we need to first calculate the variance using the formula:
Var(X) = Σ [(x - μ)^2 * P(X)]
where:
x = each value of X (0, 1, 2, 3 in this case)
μ = mean of X
P(X) = probability of each value of X
First, calculate the mean of X:
μ = Σ [x * P(X)]
μ = (0 * 0.35) + (1 * 0.35) + (2 * 0.25) + (3 * 0.05)
μ = 0 + 0.35 + 0.5 + 0.15
μ = 1
Next, calculate the variance:
Var(X) = [(0 - 1)^2 * 0.35] + [(1 - 1)^2 * 0.35] + [(2 - 1)^2 * 0.25] + [(3 - 1)^2 * 0.05]
Var(X) = (1) * 0.35 + (0) * 0.35 + (1) * 0.25 + (4) * 0.05
Var(X) = 0.35 + 0.25 + 0.2
Var(X) = 0.8
The standard deviation is the square root of the variance:
Standard deviation = √Var(X)
Standard deviation = √0.8
Standard deviation ≈ 0.894
Therefore, the standard deviation of the number of retransmissions is approximately 0.894.