New UNIT 4B

Question 1

Why is it called “binomial”

Answer 1

These numbers come from the coefficients of expanded binomials..

(x+y)¹, (x+y)², (x+y)³

Question 2

when can you expect the first success if there is a 30 percent chance of success?

(mean of geo)

Answer 2

1/p or 1/.30.

Which is 3.333 so around the 3rd or 4th try.

1/p tells you, on average, when the first success will occur

1/p is the mean of the geometric distribution

Question 3

How many successes can you expect?

(mean of binormial)

Answer 3

np.

Makes sense, if 30% like butter, out of 50 people you would expect (50)(.3)= 15 to like butter

np is the mean of the binomial distribution

Question 4

what does geometric model tell us about?

Answer 4

it is about FIRST SUCCESS

What is likelihood first success is on 5th trial?

Question 5

how do you combine probability models?

(play more than one game)

Answer 5

add or subtract the means, and then

ADD THE VARIANCE

Question 6

Do we add or subtract st dev when combining models?

Answer 6

neither

you always just add variances. Square the st devs, add them, then take sqrt.

Question 7

How do you find mean and sd of discreet random variable ?

Answer 7

put values in L1, probabilities in L2, and run “1-var stats L1,L2” and you get it!

Question 8

what is pythagorean theorem of stats?

Answer 8

st dev of combined model is: sqrt(st dev squared + st dev squared) or more if you combine more?

Question 9

What is the “mean of a random variable?”

Answer 9

The expected value. sum of probs times values

Question 10

What is the expected value?

Answer 10

The mean of the random variable. What you’d AVERAGE if you played the game A LOT!!!!!!!!!

Question 11

binopdf

(inputs)

Answer 11

EXACTLY X successes in N tries

binopdf(n,p,x).

Probability of exactly X successes in N trials. (PARTICULAR probability)

Question 12

binocdf (inputs)

Answer 12

EXACTLY X OR LESS successes in N tries

binocdf(n,p,x)..

Probability of X OR LESS successes in N trials. (CUMULATIVE probability)

Question 13

geopdf (inputs)

Answer 13

FIRST SUCCESS ON

geopdf (p,x)

probability of FIRST SUCCESS being ON the Xth trial

Question 14

geocdf (inputs)

Answer 14

FIRST SUCCESS ON OR BEFORE

geocdf(p,x).

Probability of the FIRST SUCCESS being ON OR BEFORE the Xth trial.

Question 15

How can we use Pascal’s Triangle?

Answer 15

To find probability of x successes in K trials.. BINOMIAL BABY!!!

Question 16

What type of probability when you are looking for the first success on or before the fifth attempt?

Answer 16

Geocdf(p, 5)

Question 17

What type of probability when you are looking for the first success after the fifth attempt?

Answer 17

not on the 4th or before

1 - geocdf(p, 4)

Question 18

What type of probability when you are looking for exactly 5 successes in twelve attempts?

Answer 18

binopdf (12,p,5)

Question 19

What type of probability when you are looking for exactly 5 or more successes in twelve attempts?

Answer 19

(more than 4)

1 - binocdf(12, p, 4)

Question 20

What type of probability when you are looking for exactly 5 or less successes in twelve attempts?

Answer 20

binocdf(12, p, 5)

Question 21

What type of probability when you are looking for more than 5 successes in twelve attempts?

Answer 21

6 or more same as not 5 or less

1 - binocdf(12, p, 5)

Question 22

What type of probability when you are looking for less than 5 successes in twelve attempts?

Answer 22

4 or less

binocdf(12, p, 4)

Question 23

What type of probability when you are looking for at least one success in twelve attempts?

Answer 23

1 - p(NONE)

not zero

1-binopdf(12, p, 0)

Question 24

RAND VARIABLE:

X has mean y and standard deviation of z.

A has mean b and standard deviation c.

Find: Mean, SD and VAR of: X + 12

Answer 24

mean: y+12

SD z

var: z²

Question 25

RAND VARIABLE:

X has mean y and standard deviation of z.

A has mean b and standard deviation c.

Find: Mean, SD and VAR of: 3X

Answer 25

mean: 3y

SD 3z

var 9z²

Question 26

RAND VARIABLE:

X has mean y and standard deviation of z.

A has mean b and standard deviation c.

Find: Mean, SD and VAR of: 5A

Answer 26

mean: 5b
sd: 5c
var: 25c²

Question 27

RAND VARIABLE:

X has mean y and standard deviation of z.

A has mean b and standard deviation c.

Find: Mean, SD and VAR of: 3X + 5A

Answer 27

mean: 3y+5b
sd: SQRT(9z²+25c²⁾
var: 9z²+25c² (same as (3z)² + (5z)²)

Question 28

RAND VARIABLE:

X has mean y and standard deviation of z.

A has mean b and standard deviation c.

Find: Mean, SD and VAR of: X + A

Answer 28

mean: y+b

SD SQRT(z²+c²)

var z²+c²

Question 29

RAND VARIABLE:

X has mean y and standard deviation of z.

A has mean b and standard deviation c.

Find: Mean, SD and VAR of: 3X + 5A + 12

Answer 29

mean: 3y+5b+12
sd: sqrt (9z² +25c²)

var 9z²+25c²

Question 30

RAND VARIABLE:

X has mean y and standard deviation of z.

A has mean b and standard deviation c.

Find: Mean, SD and VAR of: X + X + X

Answer 30

mean: y+y+y

sd SQRT(z²+z²+z²) ….

var (z²+z²+z²)

Question 31

What is diff between 3X and X+ X+ X

(mean and st. dev)

Answer 31

3X is just tripling one play. Mult mean and SD by 3.

X+X+X is playing 3 times, must add variances, square SD’s add 3 times then sqrt.

Question 32

If combining 4 random variables with standard deviations of m, p, q, r…. what is the new combined standard deviation?

Answer 32

SQRT(m² + p² + q² + r²)