Probstat/week8 practice 1

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This is part of probstat

This exercise considers continuous random variables.

Probability

Uniform distribution

1. Let random variable is a continuous random variable which is a real number chosen uniformly from the range (10,50). Let denote its probability distribution function.

  • 1.1 Describe .
  • 1.2 What is .
  • 1.3 What is . (Note that this is a conditional probability.)

Expectation

Definition: If is a continuous random variable whose probability distribution function (pdf) is , we define the expected value of to be