Stats Quiz 1

Number of r-permutations on n elements, where r is the number of elements you’re choosing each time.

n!/(n-r)!

Number of r-combinations on n elements (n choose r)

n!/(r! (n-r)!)

Additive law of probabilities

P(A union B)= P(A) + P(B) - P(A intersect B)

Multiplicative Rule for Probabilities (law of conditional probability)

P (A|B) = P(A intersect B)/ P(B)

Condition of Independence

P(A|B)=P(A)

Probability of set intersection if they are dependent

P(A intersect B)=P(A|B)P(B)

Probability of set intersection if they are independent

P(A intersect B)=P(A)P(B)

Law of Total Probability

If the sum of B_i forms a partition of S, then P(A) can be written as P(A)= sum of P(B_i)P(A|B_i)

Bayes Law

P(B_j|A)=P(B_j intersect A)/ (sum of P(B_i)P(A|B_i))