A student's grade in a certain course is modeled by the joint PDF below; where X is the grade of the lecture component and Y is the grade of the lab component. (6x + 10y, (0, 0sxs 0.5,0 < y s 0.5 otherwise fxx(xy) = Determine the probability that the student's grade in the lecture component is greater than the lab component
A student's grade in a certain course is modeled by the joint PDF below; where X is the grade of the lecture component and Y is the grade of the lab component. (6x + 10y, (0, 0sxs 0.5,0 < y s 0.5 otherwise fxx(xy) = Determine the probability that the student's grade in the lecture component is greater than the lab component
A First Course in Probability (10th Edition)
10th Edition
ISBN:9780134753119
Author:Sheldon Ross
Publisher:Sheldon Ross
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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Subject: Probability
Helping Tag: Statistics

Transcribed Image Text:1. Answer the following questions and write complete solutions:
a)
A student's grade in a certain course is modeled by the joint PDF below;
where X is the grade of the lecture component and Y is the grade of the
lab component.
(бх + 10y,
fxx(xy) = 1o,
0 <x< 0.5,0 <y< 0.5
otherwise
Determine the probability that the student's grade in the lecture
component is greater than the lab component
b)
A certain factory produces X, specialized parts on day n, where X, are
independent and identically distributed random variables with mean 6
and variance 9. Let S,be the total number of specialized parts produced
from day one to day n. Using Central Limit Theorem, determine the total
number of parts, a, the said factory can guarantee to produce by day 50
with at least 99.9% certainty, i.e., determine the maximum value of aso
that P(S50 2 a) 2 0.9999. Note that this maximum value must be a
whole number
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