2. (a) An electronic device has lifetime denoted by T. The device has value V=5 if it fails before time t=3; otherwise, it has value V=2T. Find the c.d.f. of V, if T has p. d. f. 1 fr(t) e¯1.5,t > 0. 1.5 = -

A First Course in Probability (10th Edition)
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Chapter1: Combinatorial Analysis
Section: Chapter Questions
Problem 1.1P: a. How many different 7-place license plates are possible if the first 2 places are for letters and...
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2. (a) An electronic device has lifetime denoted by T. The device has value
V=5 if it fails before time t=3; otherwise, it has value V=2T. Find the c. d. f.
of V, if T has p.d. f.
fr(t) = 15°
e1.5, t > 0.
1.5
(b) Suppose that the random variables X and Y have the joint p. d. f.
– y), 0 < x < 2, –x < y < x
f (x, y) = {kx(x –
elsewhere
(i)
Evaluate the constant k.
(ii)
Find the marginal p. d. f. of the two random variables.
Transcribed Image Text:2. (a) An electronic device has lifetime denoted by T. The device has value V=5 if it fails before time t=3; otherwise, it has value V=2T. Find the c. d. f. of V, if T has p.d. f. fr(t) = 15° e1.5, t > 0. 1.5 (b) Suppose that the random variables X and Y have the joint p. d. f. – y), 0 < x < 2, –x < y < x f (x, y) = {kx(x – elsewhere (i) Evaluate the constant k. (ii) Find the marginal p. d. f. of the two random variables.
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