Lesson Worksheet: Continuous Random Variables Mathematics

In this worksheet, we will practice describing the probability density function of a continuous random variable and using it to find the probability for some event.

Q1:

Let 𝑋 be a continuous random variable with probability density function 𝑓(𝑥)=18(6𝑥7)2𝑥3,0.ifotherwise Find 𝑃(2𝑋2.5).

  • A0
  • B1332
  • C1932
  • D1316

Q2:

Let 𝑋 be a continuous random variable with probability density function 𝑓(𝑥)=𝑎62𝑥,30𝑥32,0.otherwise Find 𝑃(30.5𝑋31.5).

  • A375496
  • B12
  • C127496
  • D121496

Q3:

Let 𝑋 be a continuous random variable with the probability density function 𝑓(𝑥) represented by the following graph. Find 𝑝(4𝑋5).

  • A58
  • B316
  • C916
  • D34
  • E38

Q4:

Let 𝑋 be a continuous random variable with the probability density function 𝑓(𝑥), represented by the following graph. Find 𝑝12𝑋2.

  • A13
  • B59
  • C38
  • D14
  • E516

Q5:

Let 𝑋 be a continuous random variable with the probability density function 𝑓(𝑥)=163,9𝑥72,0.otherwise Find 𝑃(𝑋>64).

  • A863
  • B463
  • C5563
  • D1663

Q6:

Let 𝑋 be a continuous random variable with probability density function 𝑓(𝑥)=16(𝑥5),7𝑥9,0.otherwise Find 𝑃(𝑋8).

  • A12
  • B512
  • C34
  • D0

Q7:

Let 𝑋 be a continuous random variable with probability density function 𝑓(𝑥)=𝑎𝑥,1𝑥5,0.otherwise Determine the value of 𝑎.

  • A12
  • B112
  • C16
  • D1112

Q8:

Let 𝑋 be a continuous random variable with probability density function 𝑓(𝑥)=4𝑥+𝑘213𝑥4,0.ifotherwise Find the value of 𝑘.

Q9:

Let 𝑋 be a continuous random variable with the probability density function 𝑓(𝑥)=𝑥8,2<𝑥<3,148,3<𝑥<36,0.otherwise Find 𝑃(11𝑋24).

  • A14
  • B7
  • C1348
  • D1,28716

Q10:

Let 𝑋 be a continuous random variable with the probability density function 𝑓(𝑥), represented by the following graph. Find the value of 𝑎 that makes 𝑃(5<𝑋<𝑎)=13.

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