The document discusses discrete probability distributions and provides examples of constructing probability distributions for random variables. A discrete probability distribution lists each possible value a random variable can take and its probability. It must have probabilities between 0 and 1 that sum to 1. Examples include coin flips and dice rolls. The document also provides practice problems for constructing probability distributions and determining if a distribution represents a discrete random variable.

2. OBJECTIV
E:
Illustrates a probability
distribution for a discrete
random variable and its
properties.

3. RANDOM
VARIABLE
It is a numeric
variable from a
random experiment
that can take on

4. Discrete
Probability
Distribution
A discrete probability
distribution lists each
possible value the random
variable can assume,
along with the probability
for that value.

5. Toss two fair coin and let X
be the number of heads
observed. Find the
probability distribution of
X.
Example 1

6. Coin 1 Coin 2
H H
H T
T H
T T
x
2
1
1
0
P(X=x)
1/4
1/4
1/4
1/4
x
P(X=x)
2
1/4
1
1/2
0
1/4

7. x
P(X=x)
2
1/4
1
1/2
0
1/4
1/4 1/2 1/4
+ + = 1
Properties of Discrete Probability Distribution
1. The sum of all the probabilities is 1:
2. The probability for each value of
the discrete random variable must
be between 0 and 1, inclusive:
ΣP X = 1
0 ≤ 𝑃(𝑋) ≤1

8. Flip 3 coins at the same
time. Let random
variable X be the heads
showing.
Example 2

9. DISCRETE PROBABILITY DISTRIBUTION
HHH
HHT
HTH
THH
HTT
THT
TTH
TTT
3 heads
2 heads
2 heads
2 heads
1 head
1 head
1 head
0 head

10. x
P(X=x)
0
1/8
1
3/8
3
1/8
DISCRETE PROBABILITY DISTRIBUTION
HHH
HHT
HTH
THH
HTT
THT
TTH
TTT
3 heads
2 heads
2 heads
2 heads
1 head
1 head
1 head
0 head
2
3/8
heads

11. Probability distribution
for X, sum of 2 rolled
dice.
Example 3

12. DISCRETE PROBABILITY DISTRIBUTION
x
P(X=x)
2 3 4 5 6 7 8 9 10 11 12
1/36 2/36 3/36 4/36 5/36 6/36 5/36 4/36 3/36 2/36 1/36

13. The discrete random variable Y has
probability distribution as shown
Example 4
Y
P(Y)
-3 -2 -1 0 1
0.1 0.25 0.3 0.15 c
Find:
a. The value of c
b. P(-3≤ 𝑌 < 0)
c. P(𝑌 > −3)
d. P(-3< 𝑌 < 1)
e. The mode

14. The probability distribution of a
random variable X, is given by
𝑃 𝑋 = 𝑥 = 𝑐𝑥2
, 𝑓𝑜𝑟 𝑥 = 0, 1, 2, 3, 4.
Given that c is a constant, find the
value of c.
Example 5

15. The probability distribution of a random variable X,
is given by 𝑃 𝑋 = 𝑥 = 𝑐𝑥2
, 𝑓𝑜𝑟 𝑥 = 0, 1, 2, 3, 4.
Given that c is a constant, find the value of c.
Example 5
X
P(X=x)
0 1 2 3 4
0 c 4c 9c 16c

18. A. Construct a probability distribution in tabular form
for the random variable described in
each situation.
1. A shipment five computers contains two
that are slightly defective. A retailer
receives three of these computers at
random. Let Z represent the number of
computers purchased by the retailer
which are slightly defective.

19. 2. Make a probability distribution table for
the numbers on the spinning wheel. Let
X be the number on the wheel.

20. B. Determine whether the distribution represents a
probability distribution for a discrete
random variable.

22. 1. A shipment five computers contains two that are slightly
defective. A retailer receives three of these computers at
random. Let Z represent the number of computers purchased
by the retailer which are slightly defective.

23. 2. Make a probability distribution table for the numbers
on the spinning wheel. Let X be the number on the
wheel.

24. B. Determine whether the distribution represents a
probability distribution for a discrete
random variable.
NO
YES

25. YES
NO
NO