chapter 6

Question 1

what are the 3 continuous random variables distributions

Answer 1

1. uniform
2. normal
3. exponential
4. normal approximation to the binomial

Question 2

what is the fundamental different b/w discrete and continuous random variables

Answer 2

how they are computed

Question 3

Explain Fx for a discrete random variable

Answer 3

provides the prob a random variable assumes a particular value

Question 4

explain Fx for a continuous random variable

Answer 4

it is the probability density function
- does not directly provide the prob of the continuous random variable x
- it does provide the continuous random variable x assumes a value in the interval
-

Question 5

for a continuous random variable, the area under th graph of f(x) at any point is

Answer 5

0

Question 6

for continuous random variables F(x) must be what for all values of x

Answer 6

> or = 0

greater than or equal to zero

Question 7

for uniform prob distribution - how do you calculate f(x)

Answer 7

1/ (b-a)

Question 8

for uniform prob distribution - how do you calculate the prob of an interval

Answer 8

(b-a)x F(x)

Question 9

For uniform prob distribution - how do you calculate expected value (or mean)

Answer 9

(a+b) / 2

Question 10

for uniform prob distribution - how do you calcualte the variance

Answer 10

(b-a)squared / 12

Question 11

if x is a continous random variable then, x can assume what

Answer 11

any value in an interval

- intervals are equally likely

Question 12

F(x) probaility density function (uniform) the area of a rectangle is

Answer 12

width x height

Question 13

What are the two major differences b/w the treatment of continous random variables and discrete random variables

Answer 13

1. we no longer talk about the prob of the random variable assuming a particular value
   - we talk about the prob of the random variable assuming a value within some given Interval
2. the prob of a continuous random variable assuming a value w/in some given interval from x1 to x2 is defined to be the
   • the area under the graph of the prob density function b/w x1 and x2

Question 14

b/c a single point of any interval of 0 width implies what

Answer 14

1. that for x to be exactly a number = 0

2. the prob of a x assuming a value in any interval is the same whether or not the end points are included

Question 15

Is the height of a density function a probability?

Answer 15

NO

Question 16

provide examples of when to use the normal prob distribution

Answer 16

a wide variety of practical applications

1. heights and weights of people
2. test scores
3. scientific measures
4. amounts of rainfall etc

Question 17

which probability density function is the most important

Answer 17

normal

Question 18

what is the normal prob distribution used as

Answer 18

a statistical inference where the normal distribution provides a description of the likely results obtained thorough sampling

Question 19

the normal curve has what shape

Answer 19

bell curve

Question 20

what are the 6 characteristics of a normal distribution

Answer 20

1. has 2 parameters (m - mean and Q - standard deviation)
2. the highest point on the curve is at the mean, which is also the median and mode
3. the mean can be any numerical value negative, o or positive
4. it is symmetric (it goes to infinity in both directions)
   - each side from the mean is the mirror image
   - skewness is zero
5. the SD determines how flat and wide the curve is
   - larger SD = wider and flatter curves (shows more variability in the data)
6. Prob(s) are given by areas under the curve
   - total area under the curve = 1

Question 21

What are some commonly used intervals for the normal distribution

Answer 21

1. 68.3% of the values of a normal random variable are w/in plus or mins 1 sd of its mean
2. 95.4 % 2 SD
3. 99.7% 3SD

Question 22

What are the characteristics of a standard NOrmal Prob Distribution

Answer 22

mean = 0
SD = 1
Z- is used to designate this particular normal random variable (z-scores convert the data to a a standard normal prob distribution so we can use z-tables to make inferences)

Question 23

what does the z-score tell us

Answer 23

how many sd it is away form the mean

- it allows us to calculate the area the z-score is associated with using z-tables

Question 24

Standardization uses the formula

Answer 24

z= x-m / SD

Question 25

Why do we use the normal approximation of the binomial probabilities

Answer 25

1. when the # of trials becomes large, evaluating the binomial prob function by hand or with a calculator is difficult

Question 26

What does a binomial experiment consist of

Answer 26

consists of a sequence of n identical independent trials with each trial having 2 possible outcomes, a success or a failure

Question 27

with a binomial experiment the prob of success on any trial is

Answer 27

the same for all trials

Question 28

what is the continuity correction error

Answer 28

.5 is added and/or subtracted to calculate the z-score

Question 29

For the binomial continuity correction error

if you want know for example 13 or fewer

Answer 29

13.5 is used to compute the z-score

Question 30

For the binomial continuity correction error

if you want know for example exactly 12

Answer 30

compute z-score for 11.5 and then 12.5 and subtract

Question 31

Exponential distribution has a mean and sd of what

Answer 31

they are equal or the same

m=sd

Question 32

for Exponential dist. how do you calculate less than or = 6

Answer 32

1-e to exponent of -6/mean

DOUBLE CHECK THIS ANSWER

Question 33

for exponential dist. how do you calculate great than 6

Answer 33

calculate less than 6 then 1 - this number

DOUBLE CHECK THIS ANSWER

Question 34

for exponential dist. how do you calcualte b/w two numbers example b/w 4 and 6

Answer 34

you first calculate using -4/m

then you do it with -6/m and subtract the two

Question 35

what is the skewness measure for the exponential distribution

Answer 35

2

and is skewed right

Question 36

how do you calculate the the sd for the exponential

Answer 36

m=Q

so

Question 37

What are some examples the exponential prob distribution used for?

Answer 37

1. time b/w arrivals at a car wash
2. time required to load a truck
3. distance b/w major defects in a highway etc

Question 38

what is the relationship b/w exponential and poisson

Answer 38

Poisson
- provides an appropriate description of the # of OCCRURRENCES per interval

Exponential
- provides a description of LENGTH of Interval b/w Occurrences

Question 39

For any continuous random variable, the probability that the random variable takes a value less than zero is

Answer 39

any number between zero and 1

Question 40

For the standard normal prob distribution, the area to the right of the mean is more than______.

Answer 40

.50

Question 41

The prob that a continuous random variable takes on any specific value is

Answer 41

0

Question 42

a normal distribution with a mean of zero and sd of 1 is called

Answer 42

a standard normal distribution

Question 43

the z score for the standard normal distribution can be

Answer 43

either negative or positive

Question 44

in a standard normal distribution, the prob that z is greater than zero is

Answer 44

0.5

Question 45

a negative value for z indicates that

Answer 45

the number of sd of an observation is to the left of the mean

Question 46

for a standard normal distribution, the prob of z is greater than zero is

Answer 46

.50 (remember the mean is 0)