Consider a random variable X having cdf FX (x) = { 1, x ≥ 2, x+1/3 , −1 < x < 2, 0, x ≤ −1.
Posted: Wed Jul 06, 2022 12:25 pm
Consider a random variable X having cdf
FX (x) = { 1, x ≥ 2,
x+1/3 , −1 < x < 2,
0, x ≤ −1.
(a) Give the pdf of X. (Note: Based on the material covered inthe 8th lecture of the semester, you should be able to concludethat the density of X is that of the uniform distribution havingmean 0.5 and variance 0.75.)
(b) Give the cdf of Y = |X|. (Note: Since g(x) = |x| is not amonotone function on the support of X, (−1, 2), the “method oftransformations” (see p. 255 of text) cannot be used. Instead, oneshould use the “cdf method” (aka, “method of distributionfunctions” (p. 253 of text)).
FX (x) = { 1, x ≥ 2,
x+1/3 , −1 < x < 2,
0, x ≤ −1.
(a) Give the pdf of X. (Note: Based on the material covered inthe 8th lecture of the semester, you should be able to concludethat the density of X is that of the uniform distribution havingmean 0.5 and variance 0.75.)
(b) Give the cdf of Y = |X|. (Note: Since g(x) = |x| is not amonotone function on the support of X, (−1, 2), the “method oftransformations” (see p. 255 of text) cannot be used. Instead, oneshould use the “cdf method” (aka, “method of distributionfunctions” (p. 253 of text)).