Description
the notes is written by hand from stat class, so I need some one know how to write in latex.
Explanation & Answer
Hello Pal, here is the solution feel free to ask for edits asap.Regards Charles
Population:(Space)
Something about this space so you ask a question
To answer this questions
• Experimaent
• Trial
event → set
• Sample
• Random
Question
(i) what is the probability that the random toss of a fair coin will land on the head.
• sample space: y = [H, T ]
• Experiment: Toss
• Event : H: the random toss lands on heads
• Computes: Probability of H, Probability(H)
• What is probability (H)?
• How is it computed or assigned?
(ii) what is the probability of drawing a defective if you pick a fruck load of tons?
* Three definitions of probability:
1 probability of an event as relative frequency of that event
Let A be an event
Probability(A)= Pr(A)=P(A)
=
lim
n→F requency(A,m)= N umberofmtimespans
E.g : P robability(Head) = P r(H) =
N umberof headbudness
N umberof losses
|Fm (A) − P (A)| <
1
2 Classical assignment of Probabilities
This definition is based on mating of combihties
Probability(A)=P(A)=
A
φ
=
N umberof f rooblecessA
N umberof possiblecases
Sizeof A
Sizeof thewholesamplespace
A ≡ size of A = cardinality of A
Hence the need for continuing using combination
E.G
Roll of fair six face die
(1) Probability(Event Number)
φ = [1, 2, 3, 4, 5, 6], φ = 6
E : ∗Eventnumberappears
E = [2, 4, 6], E = 3
P robability(E) =
E
|phi
=
31
62
3 Subjective assignment of probability(Common in Bayesian Statistics) Probability(A)=P(A)=
Degree of belief in the occurrence of A
Provided that P (A) ∈ [0, 1]
n1 , n2 , . . . , nm
L = n1 , n2 , . . . , nm
How many ways can this car be specified
If there are 7 color, 2 trans, 4 ste and 6 inter
L = 7 ∗ 2 ∗ 4 ∗ 6 = 332
3letter[a, b, c]
goal discovery of 2 letter words
(i) Repetition
3 ∗ 3 = 32 = 9
(ii) No repetition
3∗2=6
= [a, b, c, d]
form two letter words
2
n1 , n2
Without repetition[4][3] = 4 ∗ 3
with repetition[4][4] = 4 ∗ 4
Theorem 2
Let n be size of the set
n! = n ∗ (n − 1) ∗ (n − 2) ∗ . . . ∗ 2 ∗ 1
Defines the number of orderings (Arrangements/permutations) of ...