# Lesson Worksheet: Discrete Random Variables Mathematics

In this worksheet, we will practice identifying discrete random variables and using probability distribution functions and tables for them.

Q1:

Can the function in the given table be a probability distribution function?

 𝑥 𝑓(𝑥) 0 1 4 5 0.17 0.43 0.69 0.36
• ANo
• BYes

Q2:

Can the function in the given graph be a probability distribution function? • ANo
• BYes

Q3:

The function in the given table is a probability distribution function of a discrete random variable . Find the value of .

 𝑋 𝑓(𝑋) 1 2 3 4 5 15 110 310 110 𝑎
• A
• B
• C
• D
• E

Q4:

Let denote a discrete random variable that can take the values 0, 1, 2, and 3. Given that , , , and , find the value of .

• A
• B
• C
• D
• E

Q5:

Let denote a discrete random variable which can take the values 1, 2, 3, 4, 5, and 6. Given that has probability distribution function , find the value of .

• A
• B
• C
• D

Q6:

Let denote a discrete random variable which can take the values 3, 5, and 6. Which of the following functions could represent the probability function of ?

• A
• B
• C
• D

Q7:

Let denote a discrete random variable which can take the values , 2, 4 and 5. Given that , , and , find the value of .

Q8:

Given that , is a probability distribution of a discrete random variable , calculate the following.

The value of

• A
• B
• C
• D
• E

Q9:

Let be the random variable that represents the number of patients who visit a dental clinic per hour. The probability distribution of is shown in the table below.

 𝑥 𝑓(𝑥) 10 11 12 13 14 15 0.2 0.1 0.15 0.05 0.3 0.2

Find the probability of the following.

Exactly 13 patients visiting the clinic in a given hour

At least 13 patients visiting the clinic in a given hour

At most 13 patients visiting the clinic in a given hour

Q10:

In an experiment in which a fair coin is tossed five consecutive times, let be the discrete random variable expressing the number of heads minus the number of tails. Find the probability distribution of .

• A
 𝑥 𝑓(𝑥) −4 −3 −1 1 3 4 132 532 1032 1032 532 132
• B
 𝑥 𝑓(𝑥) −5 −3 −1 1 3 5 132 1032 532 532 1032 132
• C
 𝑥 𝑓(𝑥) −5 −3 −1 1 3 5 132 532 1032 1032 532 132
• D
 𝑥 𝑓(𝑥) −3 −1 0 1 3 532 1032 232 1032 532
• E
 𝑥 𝑓(𝑥) −5 −3 −1 0 1 3 5 132 532 932 232 932 532 132

This lesson includes 26 additional questions and 225 additional question variations for subscribers.