1. Let X denote the number of times a certain numerical control machine will malfunction: 1, 2, or 3 times on any given day. Let Y denote the number of times a technician is called on an emergency call. Their joint probability distribution is given below: f(x,y) 1 2 3 I y 2 3 0.05 0.02 0.05 0.20 1 0.10 0.10 0.35 0.03 0.10 t. Find the conditional distribution of f(lx), P(Y = 3 | X = 1). u. Find the conditional distribution of f(x), P(Y=3 | X = 2). v. Find the conditional distribution of f(x), P(Y=3 | X= 3).
1. Let X denote the number of times a certain numerical control machine will malfunction: 1, 2, or 3 times on any given day. Let Y denote the number of times a technician is called on an emergency call. Their joint probability distribution is given below: f(x,y) 1 2 3 I y 2 3 0.05 0.02 0.05 0.20 1 0.10 0.10 0.35 0.03 0.10 t. Find the conditional distribution of f(lx), P(Y = 3 | X = 1). u. Find the conditional distribution of f(x), P(Y=3 | X = 2). v. Find the conditional distribution of f(x), P(Y=3 | X= 3).
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Transcribed Image Text:1. Let X denote the number of times a certain numerical control machine will malfunction:
1, 2, or 3 times on any given day. Let Y denote the number of times a technician is
called on an emergency call. Their joint probability distribution is given below:
f(x,y)
1
2
3
I
2/2
3
0.10 0.05 0.02
0.35 0.05
0.10
0.03 0.10 0.20
t. Find the conditional distribution of f(ylx), P(Y=3|X= 1).
u. Find the conditional distribution of f(ylx), P(Y=3 | X = 2).
v. Find the conditional distribution of f(ylx), P(Y=3 | X= 3).
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