Mean and Variance of Random Variables MCQ

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• A Random Variable X can take only two values, 4 and 5 such that P(4) = 0.32 and P(5) = 0.47. Determine the Variance of X.
  ক

  8.21

  খ

  12

  গ

  3.7

  ঘ

  4.8
• A football player makes 75% of his 5-point shots and 25% his 7-point shots. Determine the expected value for a 7-point shot of the player.
  ক

  4.59

  খ

  12.35

  গ

  5.25

  ঘ

  42.8
• A probability density function f(x) for the continuous random variable X is denoted as _______
  ক

  ∫ f(x)dx = ∞, -1<=x<=1

  খ

  ∫ f(x)dx = 1, -∞<=x<=∞

  গ

  ∫ f(x)dx = 0, -∞<=x<=∞

  ঘ

  ∫ f(x+2)dx = .5, -∞<=x<=∞
• A jar of pickle is picked at random using a filling process in which an automatic machine is filling pickle jars with 2.5 kg of pickle in each jar. Due to few faults in the automatic process, the weight of a jar could vary from jar to jar in the range 1.7 kg to 2.9 kg excluding the latter. Let X denote the weight of a jar of pickle selected. Find the range of X.
  ক

  3.7 ≤ X < 3.9

  খ

  1.6 ≤ X < 3.2

  গ

  1.7 ≤ X < 2.9

  ঘ

  1 ≤ X < 5