2. PROPERTIES OF DISCRETE PROBABILITY DISTRIBUTION
1. The sum of all
probabilities should be 1.
2. Probabilities should be
confined between 0 and 1.
P (X) = 1
0 ≤ P (X) ≤ 1
Number of
Heads, X
0 1 2
Probability,
P(X)
1
_
4
1
_
2
1
_
4
P (X) = 1
_
4
1
_
4
1
_
2
+ + = 1
3. Example 1: Determine whether the distributions is a discrete
probability distribution.
P (X) = 1 0 ≤ P (X) ≤ 1
X 3 6 8
P(X) -0.3 0.6 0.7
a. X 1 2 3 4 5
P(X)
3
_
10
1
_
10
1
_
10
2
_
10
3
_
10
b.
No, it is not a discrete
probability distribution,
P(X) cannot be -0.3
Yes, it is a discrete
probability distribution,
4. 0
H
T
H
T
H
T
H
T
H
T
H
T
H
T
Example 3:
Supposed three coins
are tossed. Let Y be the
random variable
representing the number
of tails. Construct the
probability distribution
and draw the histogram.
Sample Space:
{ HHH, HHT, HTH, HTT,
THH, THT, TTH, TTT }
5. Example 2: Supposed three coins are tossed. Let Y be the random
variable representing the number of tails. Construct the probability
distribution and draw the histogram.
Possible
outcomes
Value of the random
variable Y (number of
tails)
HHH 0
HHT 1
HTH 1
HTT 2
THH 1
THT 2
TTH 2
TTT 3
Number of
tails, Y
0 1 2 3
P(X)
1
_
8
3
_
8
3
_
8
1
_
8
1
_
8
2
_
8
3
_
8
0
0 1 2 3
