Math Problem Solver

Random Variables and Probability Distribution Lesson 1.3 Constructing Probability of Random Variables

At the end of the lesson, you are expected to:

1. illustrate a probability distribution for a discrete random variable and its properties, 2. Identify the possible values of a

specified random variable 1. compule probabilities corresponding to a given random variable.

Steps in getting the probability of each value of the random variable: 1. Determine the sample space. Assign letters that will represent each outcome.

2. Count the number of the value of the random variable (capital letter assigned)

3. Given the total possible values of the random variable, assign probability values to each value of the random variable.

Example:

1. Suppose two coins are tossed. Let H represent heads, T represent tails and X be the random variable representing the number of heads that will occur. Find the values of the random variable X.

Possible Outcomes

Values of Random Variable X (number of heads)

2

or

HH

TH

HT

TT

0

Number of Heads (X)

Probability P(X)

0

14

1

2/4

or 1/2

1/4

The probability distribution of a discrete random variable X is:

Number of Heads (X)

Probability P(X)

0 1/4

1

1/2

2

1/4

2. Suppose there are three people to be tested in Covid-19. Let P represent positive, N represent negative and Z be the random variable representing the number of infected person that occur. Find the random variable Z.

Values of Random Variable Z (number of infected)

Possible Outcomes

PPP

PPN

PNP

NPP

3

2

2

2

NNP

NPN

1

PNN

1

NNN

0

Number of infected (Z) 0

Probability P(Z)

1/8

1

3/8

2

3/8

3

1/8

The probability distribution of a discrete random variable Z is:

Number of infected (2)

Probability P(Z)

0

1/8

1

3/8

2

3/8

3

1/8

3. Two winners will be drawn from 5 security guards (S) and 6 canteen staff (C). Let W be the random variable representing the canteen staffs. Find the values of random variable W.

Possible Outcomes

Values of Random Variable W

CC

CS

SC

SS

2

1

1

0

Statistics and Probability