AS MATHS S1 WJEC

Addition law for mutually exclusive events : P(AUB) = P(B) + P(A)

The compliment of A : 1 - P(A)

P(A) = P(AnB) + P(AUB')

Generalised addition law : P(AUB) = P(A) + P(B) - P(AnB)

Multiplacation law for INDEPENDANT  events : P(AnB) = P(A) * P(B)

Multiplacation law for DEPENDANT events : P(AnB) = P(A) * P(BIA) or P(AnB) = P(B) * P(AIB)

combinations - ORDER DOES NOT  MATTER 

AND - Multiply 

OR   -  Add 

permutations - ORDER DOES MATTER 

Number of ways!<----- FACTORIAL 

Mean = E(x) * P(x)

Variance = E(x) * P(x) - mean squared 

Standard Deviation = SQUARE ROOT OF VAR(X)

Y = aX - b 

Mean = E(aX + b) = aE(X) + b 

Variance = (aX = b ) = a squared * Var(X)

BINOMIAL DISTRIBUTION :

1). n, fixed identical trials

2). trials are independant

3).each trial has 2 outcomes

4). Want to find P(success and in n trials)

POISSON DISTRIBUTION :

1). The experiment results in outcomes that can be classified as successes or failures.

2).The average number of successes (μ) that occurs in a specified region is known.

3).The probability that a success will occur is proportional to the size of the region.

4).The probability that a success will occur in an extremely small region is virtually zero.

 ----> POISSON FORMULA

  ---> BINOMIAL FORMULA 

MEAN AND VARIANCE OF THE BINOMIAL AND POISSON DISTRIBUTIONS

BINOMIAL :

E(X) = np

Var(X)= np * (1-p)

Standard Deviation = Square root of mean squared

POISSON:

Var(aX+b) = a squared * Var

E(aX+b) = aE(X) + b