[MAT2017] Probability & Statistics
Final Report
Dept. :
Student No. :
Prof. : Yoo, Doo-Yeol
Name :
[1] Continuous random variables X and Y have a joint probability density function 𝑓(𝑥, 𝑦) =
sin 𝑦 𝑒
X
for 0 < 𝑥 < ∞ and 0 < 𝑦 < 1. Find 𝑃 𝑋 > 1 𝑌 =
[2] The probability density function is given by 𝑓(𝑥) = 10𝑒
mean?
(
. )
for x ≥ 7.5. What is the
[3] The random variables X, Y, and Z have the joint probability density function, (𝑥, 𝑦, 𝑧) =
8𝑥𝑦𝑧, for 0 < x < 1, 0 < y < 1, and 0 < z < 1. (a) Please determine the conditional probability
distribution of X given that Y = 0.5 and Z = 0.8, and (b) 𝑃(𝑋 < 0.5|𝑌 = 0.5, 𝑍 = 0.8)
[4] Two methods of measuring surface smoothness are used to evaluate a paper product. The
measurements are recorded as deviations from the nominal surface smoothness in coded
units. The joint probability distribution of the two measurements is a uniform distribution
over the region 0 < x < 4, 0 < y, and x - 1 < y < x + 1. That is, fXY (x, y) = c for x and y in the
region. Please determine the following.
(a) Value for c such that fXY (x, y) is a joint probability density function.
(b) Marginal probability distribution of X
(c) Conditional probability distribution of Y given X = 1