Question

discrete random variables http://prntscr.com/32f63c

Answer 1

@ganeshie8 @Ashleyisakitty @sourwing

Answer 2

for part a)
add up all the probabilities, u should get 1

Answer 3

how can i verify?

Answer 4

if u dont get 1, then its not a legitimate distribution

Answer 5

addup the numbers in second row

Answer 6

numbers in second row represent probabilites

Answer 7

yes it equals 1

Answer 8

and also notice that probability for each outcome is between [0, 1]

Answer 9

thats all we need for part a?

Answer 10

based on those "two" observations, we can conclude that the given distribution is legitimate

Answer 11

yes, a distribution needs to satisfy below :
1) each probability is between [0, 1]
2) probabilities addup to 1

Answer 12

since u have verified that it satisfies both, conclude that its legitimate and move on

Answer 13

oh i didnt know that! how simply!

Answer 14

@Luigi0210

Answer 15

@ do you know what the notation of P(X>2) is in words?

Answer 16

X is the random variable here

Answer 17

"X" represents "number of cars an American family owns"

Answer 18

replace X wid above and read

Answer 19

what would that be for letter d?

Answer 20

1?

Answer 21

first interpret wat d is asking

Answer 22

P(1>2) ?

Answer 23

P( X > 2)

Answer 24

find P(X>2)

Answer 25

P(number of cars an American family owns > 2)

Answer 26

when did i say x is 1 ?

Answer 27

i thought you did. would it be 5?

Answer 28

or do you go from 1 to 5

Answer 29

go thru our discussion above

Answer 30

what is x

Answer 31

probability can never be greater than 1
so, 5 makes no sense for part d

Answer 32

X is a random variable,
"X" represents "number of cars an American family owns"

Answer 33

okay, how would you answer this? interpret in words the notation P(X-2)?

Answer 34

P(x>2)

Answer 35

and P(X=2)

Answer 36

replace "X" wid "number of cars an American family owns"
and read

Answer 37

“P(X = 2)” is shorthand for the following: “P(A), where A denotes the set of outcomes at which the
random variable X takes the value?

Answer 38

P(X = 2)

replace X wid "number of cars an American family owns"

Answer 39

you wud get :

P("number of cars an American family owns" = 2)

Answer 40

so would that be your answer?

Answer 41

P(X = 2) represents
the probability for "number of cars an American family owns" is 2

Answer 42

that makes better sense

Answer 43

In words :

if u randomly select a family from American population, the probability for that family to own exactly 2 cars is represented by :
P(X=2)

Answer 44

well thank you kind person your a saint!!! what i dont understand is what the > is in P(x>2)

Answer 45

and how to find P(X>2)

Answer 46

">" means "greater than"

Answer 47

of course

Answer 48

P(X > 2) represents : probability for a family to have MORE THAN TWO CARS

Answer 49

that makes sense. i feel dumb.

Answer 50

finding P(X>2) is easy,
simply add the probabilities in ur second row that represent X =3 , 4, 5

Answer 51

http://prntscr.com/32faea

Answer 52

add those

Answer 53

.2 sir

Answer 54

P(0.2>2)?

Answer 55

P(X > 2) = 0.2

Answer 56

dont mess wid "X" inside parenthesis ok

Answer 57

i was just doing algebra work so i all about changing x and y lol but your awesome and really smart.

Answer 58

it should be read as :

P(X > 2) = 0.13 + 0.05 + 0. 02
= 0.2

Answer 59

http://prntscr.com/32fasn

Answer 60

lol no, you're smart !

that means there is 20% chance for finding a family wid MORE THAN 2 cars

Answer 61

how would this relate to this?

Answer 62

hint : probabilities add up to 1

Answer 63

I would say i come from a long line of rocket scientist test monkeys.

Answer 64

monkeys are fun

Answer 65

and intelligent and mischevious lol

Answer 66

okay add up all the given probabilities and subtract from 1

Answer 67

.85

Answer 68

say, P(X = 3) is \(k\)

Answer 69

you have well spent your life studying and becoming a genius at solving anything thrown at you, you have a gift sir!

Answer 70

since all the probabilites must add up to 1, we have :

\(0.4 + 0.1 + t + 0.15 + 0.2 = 1\)

Answer 71

solve \(t\)

Answer 72

t = .15

Answer 73

\(\large \color{red}{\checkmark}\)

Answer 74

hell no, im dumb on many things lol but i see you're great at learning stuff :)

Answer 75

thank you (: