HUMSS memes

HUMMS memes #20

SUBJECT: STATISTICS AND PROBABILITY

Lesson 1: Random Variables

● Measures of Central Tendency (Singit ko lang to saglit hehe)

→ MEAN - A measure of central tendency calculated by dividing the sum of all values by the number of valued in the data set (Data set is the collectiom of observations on one or more variables)
Note: Average and mean are the same. 😅

Example:
Ang data set ay {1,2,3,4,5}. Add naten sila, 1+2+3+4+5 = 15 ← Divide naten to sa 5 since 5 yung data na nasa set. 15 ÷ 5 = 3 ← Tadaaah!  Eto na po mean 😂

→ MEDIAN - The value of the middle term in a ranked data set. The median divides a ranked data set into two equal parts.

Example:
Yung sample set naten ule ay katulad sa taas, but ramble kunwari. {5,3,2,4,1} Hindi mo pwedeng kunin ang median if di nakaarrange ang numbers from lowest to highest value.

Data Set
1
2
3 → This will be your median. Basic
4
5

● MODE - The value (or values) that occurs with highest frequency in a data set.

Example:
Ang data set kunwari ay {1,2,3,3,4,4,4,5}. May pinakamadaming bilang yung value na 4 kaya it will be your Mode.

(Prerequisite ng Subject na Practical Research 2 itong Stats kaya most likely, etong central tendency ang madalas na magamit sa pagcocompute or pag-aarange ng data.)

● RANDOM VARIABLE
→ A random variable is a numerical quantity that is generated by a random experiment.
→ A random variable, usually written X, is a variable whose possible values are numerical outcomes of a random phenomenon.

● Types of Random Variable
→ Discrete Variable - is a (quantitative) variable whose values are countable.
Example: number of defective cellphones

→ Continuous Variable - is a (quantitative) variable that can assume any numerical value over a certain interval or intervals. It represents measured data. (length, height, and weight)

■ Sample Space is the set of all possible outcomes of an experiment.
X = {Head, Tails} = {0,1}
The possible values are 0 and 1.

● PROBABILITY DISTRIBUTION
→ It consists of the values of random variable assumed and the corresponding probabilities.

Example:
Suppose three coins are tossed. Let T be the random variable representing the number of tails that occur. Find the probability of each of the values of the random variable T.

Sample space is {TTT, TTH, THT, HTT, HHT, HTH, THH, HHH}

(Nasa baba ang step by step procedure to solve the given example above.)

● CONSTRUCTING A PROBABILITY DISTRIBUTION
1) Count the number of tails in each outcome and assign a number for each.
(Note: Imaginin niyo na lang na table yung baba. Mas organize kase if itetable of at least may categories for each numbers para di malito. SS stands for Sample Space, T for Tail and H for Head)

SS ||| No. of tails
TTT         3
TTH         2
THT         2
HTT         2
HHT         1
HTH         1
THH         1
HHH         0

2) Assign the Probability Values P(T) to each values. (Lista naten sa baba yung mga values na nakuha naten and kung ilan ang outcomes per sample)
Table kunwari yung sa baba xD

T   |    P(T)
3   |    1/8 or 0.125
2   |    3/8 or 0.375
1   |     3/8 or 0.375
0   |     1/8 or 0.125
         = 8/8 or 1 >> Kapag nag-exact sa 1 yung sagot niyo, tama kayo. Haha

3) Probability values can be with fractions or decimals representing the occurrence of the variable on the outcomes.
(Note: Mas madali iinterpret ang data or pinakafinal answer kapag decimal, round off na lang naten lalo na kapag madaming numbers.)

Final Answer:
If you tossed three coins, there are 13% of chances that 3 tails and 0 tail will be the outcome and there are also 38% of chances that 2 tails and 1 tail will be the result. (Yung decimal ay ginawang percent hehez baka malito)

● PROPERTIES OF A PROBABILITY DISTRIBUTION
1) The probability of each value of the random variable must be between or equal to 0 and 1.
2) The sum of the probabilities of all values of the random variable must be equal to one.

:) Madali lang yung lesson kung makikinig tayo. Sorry sa paliwanag, sana naintindihan niyo no. Hahaha

PS. Nagsave na ko copy XD