5. Let X be a random variable with distribution function   Plot the graph of F(x) and then evaluate E(x).

6. There are two classes of Probability and Statistics course. The problems of the final exam are identical for the two classes. Let μ₁ and μ₂ denote the population means of scores of class A and class B, respectively, and σ₁ and σ₂ denote the population variances of scores of class A and class B, respectively. A random sample of 13 students are taken from class A and 11 students are taken from class B. The sample average and standard deviation of scores of each class are class A: X̄ₐ = 84, Sₐ = 4 and class B: X̄բ = 77, Sբ = 6. Test whether the population means of scores of the two classes are equal. Make assumptions if necessary.

5. Let X be a random variable with distribution function

Plot the graph of F(x) and then evaluate E(x).

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