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 mean or expected value for the number of retransmissions is?
A)1.2
B)1.0
C)1.5
D)2.25
To find the mean or expected value for the number of retransmissions, we need to multiply each value of X by its corresponding probability and then sum them up.
Mean (μ) = Σ(X * P(X))
= (0 * 0.35) + (1 * 0.25) + (2 * p) + (3 * 0.15)
= 0 + 0.25 + 2p + 0.45
= 0.7 + 2p
Since the probabilities must add up to 1,
0.35 + 0.25 + p + 0.15 = 1
0.75 + p = 1
p = 0.25
Substitute p = 0.25 back into the mean formula:
Mean (μ) = 0.7 + 2(0.25)
Mean (μ) = 0.7 + 0.5
Mean (μ) = 1.2
Therefore, the mean or expected value for the number of retransmissions is A) 1.2.