probabllity and statistics

11.  Thus a random variable can be thought of as a
measurement (yielding a real number) on an
experiment
◦ Maps “events” to “real numbers”
◦ We can then talk about the pdf, define the
mean/variance and other moments

14. Number of
marbles in a jar
Discrete R.V

28. A police detective might want to know the probability of
getting a lead in a crime case after 10 people are questioned.

29. 2
)(
2
1
2
1
)( 





x
exf
This is a bell shaped curve with
different centers and spreads
depending on  and 

31. 1. The mean, median, and mode are equal.
2. The normal curve is bell-shaped and symmetric
about the mean.
3. The total area under the curve is equal to one.
4. The normal curve approaches, but never touches
the x-axis as it extends farther and farther away
from the mean.
x
Total area = 1
μ
31 Larson/Farber 4th ed

32. Standard normal distribution
 A normal distribution with a mean of 0 and a
standard deviation of 1.
3 12 1 0 2 3
z
Area = 1
Value - Mean -
Standard deviation
x
z


 
• Any x-value can be transformed into a z-score by
using the formula
32 Larson/Farber 4th ed

33.  If each data value of a normally distributed random
variable x is transformed into a z-score, the result
will be the standard normal distribution.
Normal Distribution
x

0
1
z
Standard
Normal
Distribution-x
z



• Use the Standard Normal Table to find the
cumulative area under the standard normal curve.
33 Larson/Farber 4th ed

34.  To represent the distribution of continuous
variable like-height,weight,blood pressure
etc..
Normal distribution has significant use in
statistical quality control.
Also used to aproximating discrete
distribution like bionomial distribution for
large value “n”

38. Russian mathematician Andrey Markov.

39. The children's games Snakes and Ladders , Auction, Ball game