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Material Type: Exam; Professor: Chen; Class: Probability; Subject: (Mathematics); University: University of Houston; Term: Unknown 1989;
Typology: Exams
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2 and Y = 3X + 2. Find E(Y ), V (Y ). Problem 5: Let the pdf of X be
f (x) =
{ ax, 0 ≤ x ≤ 2; 0 , otherwise.
(a) Determine the value of a. (b) Compute P (0. 5 < X ≤ 1 .5). (c) Find cdf of X. (d) Compute E(X) and V (X). Problem 6: Assume that pdf of X is f (x) = 2e−^2 x, x ≥ 0; f (x) = 0 otherwise. Find MX (t). Use MX (t) to compute E(X), V (X).
Problem 7: In a city, 10% of the population do not have medical in- surance. A random sample of 400 people is selected. What is the probability that the number of uninsured people is between 30 and 70 (inclusive). Problem 8: Suppose X has uniform distribution on [0, 1] and pdf of Y is fY (y) = 3e−^3 y^ , y ≥ 0; fY (y) = 0, otherwise. Is there a map g such that Y = g(X)?