Nagwa uses cookies to ensure you get the best experience on our website. Learn more about our Privacy Policy.

Lesson: Continuous Random Variables

Sample Question Videos

Worksheet • 25 Questions • 1 Video

Q1:

Let 𝑋 be a continuous random variable with probability density function Find the value of π‘˜ .

Q2:

Let 𝑋 be a continuous random variable with the probability density function Find 𝑃 ( 1 1 ≀ π‘₯ ≀ 2 4 ) .

  • A 1 3 4 8
  • B 1 2 8 7 1 6
  • C 1 4
  • D7

Q3:

Let 𝑋 be a continuous random variable with the probability density function Find 𝑃 ( 1 4 ≀ π‘₯ ≀ 1 5 ) .

  • A 1 4 2
  • B14
  • C 2 2 1
  • D 5 7 8

Q4:

Let be a continuous random variable with probability density function Find .

  • A
  • B0
  • C
  • D

Q5:

Let 𝑋 be a continuous random variable with probability density function Find 𝑃 ( 𝑋 ≀ 8 ) .

  • A 5 1 2
  • B 3 4
  • C0
  • D 1 2

Q6:

Let 𝑋 be a continuous random variable with probability density function Find 𝑃 ( 3 0 . 5 ≀ π‘₯ ≀ 3 1 . 5 ) .

  • A 1 2
  • B 1 2 1 4 9 6
  • C 3 7 5 4 9 6
  • D 1 2 7 4 9 6

Q7:

Let 𝑋 be a continuous random variable with the probability density function Find the value of π‘Ž .

  • A 1 1 0
  • B10
  • C 1 5
  • D 9 1 0

Q8:

Let 𝑍 be a standard normal random variable. Determine π‘˜ , given that 𝑃 ( βˆ’ 2 . 9 8 ≀ 𝑍 ≀ π‘˜ ) = 0 . 7 0 7 4 .

Q9:

Let 𝑋 be a continuous random variable with probability density function Find 𝑃 ( 𝑋 > 4 ) .

  • A 7 1 2
  • B 1 1 1 2
  • C 1 0 2 7
  • D 1 6

Q10:

Let 𝑋 be a continuous random variable with probability density function Find the value of π‘˜ .

Q11:

Let 𝑋 be a continuous random variable with probability density function Find 𝑃 ( 3 ≀ π‘₯ ≀ 4 ) .

  • A 2 9 1 0 0
  • B 1 4
  • C 9 1 0 0
  • D 3 3 1 0 0

Q12:

Let 𝑋 be a continuous random variable with the probability density function Find 𝑃 ( 𝑋 > 6 4 ) .

  • A 8 6 3
  • B 4 6 3
  • C 5 5 6 3
  • D 1 6 6 3

Q13:

Let 𝑋 be a continuous random variable with probability density function Determine the value of π‘Ž .

  • A 1 1 2
  • B12
  • C 1 6
  • D 1 1 1 2

Q14:

Let 𝑋 be a continuous random variable with probability density function Find the value of π‘˜ .

  • A 1 7
  • B 1 2 1
  • C 3 4
  • D4

Q15:

Let 𝑋 be a continuous random variable with probability density function Find 𝑃 ( 4 . 5 ≀ 𝑋 ≀ 7 ) .

  • A 6 5 1 4 4
  • B 7 1 6
  • C1
  • D 1 9

Q16:

Let 𝑋 be a continuous random variable with probability density function Given 𝑃 ( π‘Ž ≀ 𝑋 ≀ π‘Ž + 2 ) = 5 1 2 and π‘Ž ∈ [ 2 , 6 ] , determine the value of π‘Ž .

Q17:

Let be a continuous random variable with probability density function Find .

  • A
  • B
  • C
  • D

Q18:

Calculate the probability density function at π‘₯ = 1 for an exponential distribution with πœ† = 1 .

Q19:

Let 𝑋 be a continuous random variable with probability density function Given 𝑃 ( 𝑋 ≀ π‘Ž ) = 7 1 1 4 8 and π‘Ž ∈ [ 3 , 4 ] , determine the value π‘Ž .

Q20:

Let 𝑋 be a continuous random variable with probability density function Find 𝑃 ( 𝑋 > 4 . 5 ) .

  • A 7 1 6
  • B 3 3 1 6
  • C 1 5 1 6
  • D 3 4

Q21:

Let 𝑋 be a continuous random variable with probability density function Given that 𝑃 ( 1 3 < 𝑋 < π‘Ž ) = 1 3 5 0 , find the value of π‘Ž .

Q22:

Let 𝑋 be a continuous random variable with the probability density function Find 𝑃 ( 2 ≀ π‘₯ ≀ 2 . 5 ) .

  • A 7 1 3 6 8
  • B 7 1 7 3 6
  • C 2 9 7 3 6 8
  • D0

Q23:

Suppose that 𝑍 is a standard normal random variable. Given that 𝑃 ( 𝑍 β‰₯ π‘˜ ) = 0 . 4 4 8 3 , find π‘˜ using the standard normal distribution table.

Q24:

Let 𝑋 be a continuous random variable with probability density function Find 𝑃 ( 𝑋 = 3 7 ) .

  • A 1 4 0
  • B 3 2 0
  • C 1 7 2 0
  • D 3 1 0

Q25:

Let π‘₯ be a continuous random variable with probability density function Find the value of π‘˜ .

  • A 1 2 8
  • B 2 7 2 8
  • C βˆ’ 1 2 8
  • D 1 5 6
Preview