Further Stats Chapter 1: Discrete Random Variables

10 flashcards · Mathematics · by TheoTyson

1. What is a discrete random variable?

   A variable whose value depends on a random event and can only take certain numerical values.

2. What is the expected value?

   The mean of observations from a discrete random variable.

3. What is the formula for the expected value of a discrete random variable ( XXX )?

   EEE (X)(X)(X) =Σ x= \Sigma \, x=Σx ∗*∗ PPP (X=x)(X = x)(X=x)

4. What do all of the probabilities of a discrete random variable add to?

   Σ\SigmaΣ PPP (X=x)(X = x)(X=x) =1= 1=1

5. What is the formula for the expected value of a discrete random variable ( X2X^2X2 )?

   EEE (X2)(X^2)(X2) === Σ\SigmaΣ x2x^2x2 ∗*∗ P(X=x)P (X = x)P(X=x)

6. What is the formula for the variance of a discrete random variable (X)(X)(X) ?

   Var (X)(X)(X) = EEE (X2)(X^2)(X2) −-− (E(E(E (X)(X)(X) )2)^2)2

7. What is the expected value of g(X)g(X)g(X) ?

   E(g(X))=ΣE(g(X)) = \SigmaE(g(X))=Σ g(x)g(x)g(x) ∗*∗ PPP (X=x)(X = x)(X=x)

8. Simplify E(aX+b)E(aX + b)E(aX+b)

   aE(X)+baE(X) + baE(X)+b

9. Simplify E(X+Y)E(X + Y)E(X+Y)

   E(X)+E(Y)E(X) + E(Y)E(X)+E(Y)

10. Simplify Var (aX+b)(aX + b)(aX+b)

    a2a^2a2 Var (X)(X)(X)