Day Two
Means and Variances of Random variables
p. 486 23,24,26,27
p. 490 31-34

  x
x 
x
2
xi p
i
i
 x  p
2
i
Found on formula card!
Let x be the number of courses for which
a randomly selected student at a certain
university is registered.
X
1
2
3
4
5
6
7
P(X).02 .03 .09 .25 .40 .16 .05
What is the mean and standard
deviations of this distribution?
  4.66
&
 = 1.2018


Write out a probability Distribution for the
random variable x = sum
Use µx=Σxip(xi) to calculate the expected value
Here’s a game:
If a player rolls two dice
and gets aAsum
of 2is or
12,
fair game
one where
the cost to play EQUALS
he wins $20.theIf
he
gets
a
expected value!
0 $5. 5The cost
20
7,X he wins
to
P(X)
7/9
1/6
1/18
roll the dice one time is
$3. Is this game fair?
NO, since  = $1.944 which is less
than it cost to play ($3).

x = payoff
x
0
500
P(x)
.999
.001
The Practice of Statistics, Third edition - Content