Exercises for Random Variable, Exercises of Probability and Statistics

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1. A farmer has 3 rice mill machines which he usually uses to turn grain into rice. It is

estimated that the machine can last for the next 7 years. If X represents the state of the

machine that will fail in the next 7 years, determine:

a. The set of all possible combinations that will occur in the next 7 years

b. The sample space of the random variable X!

c. 𝑷(𝟏 ≤ 𝑿 ≤ 𝟑)!

(by : Fadhil)

2. The random variable X represents the number of draws in a toss of four coins. Find :

a. Set of possible

b. Sample space

c. The value of P(X=2)

(by : Najwa)

3. Erinda throws two dice once. The random variable Y represents the product of the two

dice. Determine :

a. The sample space of the random variable Y!

b. P(8≤X≤10)

( by : Tya )

4. Nico and John rolled two dice at the same time. Let X be a random variable which

denotes that the sum of the two dice is a multiple of 2. Draw a table of P(4≤X≤10)

( by : Erinda )

5. Two balanced dice are tossed simultaneously. Known:

𝟏

𝟐

𝟑𝟔

Find 𝑿(𝑺

𝒊

) if:

a. 𝑿(𝑺

𝟏

𝟐

𝟑

𝟑𝟓

𝟑𝟔

b. 𝑿(𝑺

𝟏

𝟐

𝟑

𝟑𝟓

𝟑𝟔

c. 𝑿(𝑺

𝟏

𝟐

𝟑

𝟑𝟓

𝟑𝟔

( by : Ilham )