32: Statistics - Discrete Random Variables
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Discrete Random Variables
Discrete Random Variables
01 Introduction
01 Introduction
02 Exploration 1 Part 1
02 Exploration 1 Part 1
The Expected Value E(X)
The Expected Value E(X)
03 The Expected Value E(X)
03 The Expected Value E(X)
04 Example
04 Example
The Variance Var(X)
The Variance Var(X)
05 The Variance Var(x)
05 The Variance Var(x)
06 Example
06 Example
07 Exploration 1 Part 2
07 Exploration 1 Part 2
E(aX+b) = aE(X) + b
E(aX+b) = aE(X) + b
08 E(X) Exploration
08 E(X) Exploration
09 E(aX+b)
09 E(aX+b)
10 Example
10 Example
Var(aX+b) = a²Var(X)
Var(aX+b) = a²Var(X)
11 Var(X) Exploration
11 Var(X) Exploration
12 Var(aX+b)
12 Var(aX+b)
13 Example
13 Example
E(X+Y) = E(X) + E(Y) and Var(X+Y) = Var(X) + Var(Y)
E(X+Y) = E(X) + E(Y) and Var(X+Y) = Var(X) + Var(Y)
14 E(X+Y) & Var(X+Y) Exploration
14 E(X+Y) & Var(X+Y) Exploration
15 E(X+Y) & Var(X+Y) + EXTENSION Proof
15 E(X+Y) & Var(X+Y) + EXTENSION Proof
16 EXTENSION Follow-up Proofs
16 EXTENSION Follow-up Proofs
17 E(X±Y) & Var(X±Y)
17 E(X±Y) & Var(X±Y)
18 Example
18 Example
19 E(aX+bY) & Var(aX+bY)
19 E(aX+bY) & Var(aX+bY)
20 Example
20 Example