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 0 1 4 5
𝑓(𝑥) 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 𝑋. Find the value of 𝑎.

𝑋12345
𝑓(𝑋)15110310110𝑎
  • A110
  • B12
  • C710
  • D310
  • E25

Q4:

Let 𝑋 denote a discrete random variable that can take the values 0, 1, 2, and 3. Given that 𝑃(𝑋=0)=19, 𝑃(𝑋=1)=49, 𝑃(𝑋=2)=𝑎, and 𝑃(𝑋=3)=3𝑎, find the value of 𝑎.

  • A19
  • B49
  • C59
  • D89
  • E69

Q5:

Let 𝑋 denote a discrete random variable which can take the values 1, 2, 3, 4, 5, and 6. Given that 𝑋 has probability distribution function 𝑓(𝑥)=𝑎𝑥5, find the value of 𝑎.

  • A1021
  • B57
  • C215
  • D521

Q6:

Let 𝑋 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 𝑋?

  • A𝑓(𝑥)=𝑥+310
  • B𝑓(𝑥)=𝑥28
  • C𝑓(𝑥)=45𝑥+2
  • D𝑓(𝑥)=4𝑥+52

Q7:

Let 𝑋 denote a discrete random variable which can take the values 2, 2, 4 and 5. Given that 𝑃(𝑋=2)=0.15, 𝑃(𝑋=2)=0.43, and 𝑃(𝑋=4)=0.25, find the value of 𝑃(𝑋>2).

Q8:

Given that 𝑓(𝑥)=115𝑥, 𝑥{1,2,3,,𝑘} is a probability distribution of a discrete random variable 𝑋, calculate the following.

The value of 𝑘

𝑃(2𝑋<4)

  • A35
  • B1415
  • C45
  • D115
  • E13

Q9:

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

𝑥101112131415
𝑓(𝑥)0.20.10.150.050.30.2

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 𝑋 be the discrete random variable expressing the number of heads minus the number of tails. Find the probability distribution of 𝑋.

  • A
    𝑥431134
    𝑓(𝑥)13253210321032532132
  • B
    𝑥531135
    𝑓(𝑥)13210325325321032132
  • C
    𝑥531135
    𝑓(𝑥)13253210321032532132
  • D
    𝑥31013
    𝑓(𝑥)53210322321032532
  • E
    𝑥5310135
    𝑓(𝑥)132532932232932532132

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

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