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🎤 Vocab

Small summary

p=0.4, q=0.8
States:

Active Nodes
- Send (S): p=0.4
- Not Send (NS): 1-p
Inactive Nodes
- Inactive: 1-q = 1-0.8 = 0.2
- Active & Send: qp
- Active & Not Send: q(1-p)

Epoch i = time i
= number of collisions at epoch i
= number of active notes at the end of epoch i

Assume given
Probability of 0, 1, or 2 collision?

You can't use 'macro parameter character #' in math mode\displaylines{ P(A|B) = \frac{P(A \cap B)}{P(B)} \\ P(x_2 | x_1= 1)= \frac{P(x_2 = 1 \cap x_1 = 1)}{P(x_1)} \\ P(x_1 = x_2) = P(x_1 = x_2 = 0) + P(x_1 = x_2 = 1) + P(x_1 = x_2 = 2) \\ 2p(1-p)\;[2pq(1+p) + (1-p)(1-q)] \\ + (p^2 + (1-p)) \; [p^2 + (1-p)^2] \\\\ \text{Note that: }\; 2p(1-p) = P(x_1=1) \\ [2pq(1+p) + (1-p)(1-q)] = P(x_2 = 1| x_1 = 1) \\ (p^2 + (1-p)) = P(x_1 = 2) \\ [p^2 + (1-p)^2] = P(x_2 = 2 | x_1 = 2) \\\\ P(c=0 \cap x_1=x_2) = a + b \\ P(c=0 \cap x_1=x_2 = 1) = 2p(1-p)\;[2pq(1+p) + (1-p)(1-q)] = a\\ P(c=0 \cap x_1=x_2 = 2) = (1-p)^2(1-p)^2 = b\\\\ P(c=0 | x_1 =x_2) \\ P(c=1 | x_1 =x_2) \\ P(c=2 | x_1 =x_2) \\ }$$ ## 🧪-> Example - List examples of where entry contents can fit in a larger context ## 🔗 -> Related Word - Link all related words