Question

The numThe number of cars an American family owns follows the distribution below:

Number of Cars 0 1 2 3 4 5
Probability 0.09 0.36 0.35 0.13 0.05 0.02


a) Verify that this is a legitimate probability distribution.
b) Interpret (in words) the notation P(X > 2).
c) Interpret (in words) the notation P(X = 2).
d) Find P(X > 2). (5 points)

Answer 1

for a distribution to be legitimate, it must satisfy below :
1) probabilities must add up to 1
2) each probability must be between [0, 1]

Answer 2

test whether the given distribution satisfies both conditions

Answer 3

0.09+0.36+0.35+0.13+0.05+0.02=1

Answer 4

also each probability is between [0, 1]
so its a legitimate distribution

Answer 5

for part b)

Answer 6

ok

Answer 7

can u tell me what "X" represents here ?

Answer 8

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

right ?

Answer 9

So, wat does P(X > 2) represent ?

Answer 10

not sure

Answer 11

give ur best try

Answer 12

think a bit and may be say something

Answer 13

b. 0.09+0.36+0.35+0.13=0.93

Answer 14

or 0.09+0.02=0.11

Answer 15

nope,
we dont need to do any calculaitons for parts b and c

Answer 16

we just need to interpret what the given expression means, thats all

Answer 17

b) Interpret (in words) the notation P(X > 2).

Answer 18

wat does the P(X > 2) mean ?

Answer 19

x is greater than 2

Answer 20

yes, wat does "X" represent here ?

Answer 21

the numbers of cars

Answer 22

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

Answer 23

so, P(X > 2) represents the "Probability for number of cars an American family owns is MORE THAN 2"

Answer 24

thats what P(X > 2) means okay ?

Answer 25

can u do part c similarly ?

Answer 26

c) Interpret (in words) the notation P(X = 2).

Answer 27

wat does P(X = 2) represent ?

Answer 28

c. so P(X=2) the probability number of cars an american family owns equal to 2

Answer 29

you got it !

Answer 30

wat about part d ?

Answer 31

for this part, u need to do calculation

Answer 32

d. 0.09+0.02=0.11

Answer 33

how ?

Answer 34

d) Find P(X > 2). (5 points)

Answer 35

P(X > 2) = P(X = 3) + P(X = 4) + P(C = 5)
= ?

Answer 36

add the first and last number or add 0.09
0.36+0.35+0.13=0.93

Answer 37

nope,
btw why wud u do that ?

Answer 38

ok

Answer 39

the question is asking us to find probability for having MORE THAN TWO cars

Answer 40

that means u need to add probabilities for having 3 or 4 or 5 cars ok ?

Answer 41

0.35+0.13+0.05+0.02=.55

Answer 42

not quite,
u should not add P(X = 2)

Answer 43

u need add oly 3 or 4 or 5 cars probabilities

Answer 44

0.13+0.05+0.02=0.37

Answer 45

0.13 + 0.05 + 0.02 = 0.2

Answer 46

you should get 0.2

Answer 47

yes

Answer 48

thanks

Answer 49

np :)