This document discusses properties of discrete probability distributions. It states that in a discrete probability distribution, the sum of all probabilities must be 1 and each probability must be between 0 and 1. It provides an example of a probability distribution where the number of heads from coin tosses is the random variable. It also gives an example of determining if a set of values is a valid discrete probability distribution. Finally, it presents an example of constructing a probability distribution for the number of tails when three coins are tossed.

1. PROPERTIES OF DISCRETE
PROBABILITY
DISTRIBUTION
MS. MA. JACQUELYN L. MACALINTAL
MAED STUDENT
ADVANCED STATISTICS

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

6. - Anonymous