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

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Subject: Probability Helping Tag: Statistics
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
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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