2 0.05 0.14 0.32 (a) What is P(X = 1 and Y = 1)? P(X= 1 and Y= 1) = (b) Compute P(X ≤ 1 and Ys 1). P(X ≤ 1 and Y ≤ 1) = [ (c) Give a word description of the event (X= 0 and Y# 0}. O At least one hose is in use at both islands. One hose is in use on both islands. At most one hose is in use at both islands. O One hose is in use on one island. Compute the probability of this event. P(X= 0 and Y# 0) =
2 0.05 0.14 0.32 (a) What is P(X = 1 and Y = 1)? P(X= 1 and Y= 1) = (b) Compute P(X ≤ 1 and Ys 1). P(X ≤ 1 and Y ≤ 1) = [ (c) Give a word description of the event (X= 0 and Y# 0}. O At least one hose is in use at both islands. One hose is in use on both islands. At most one hose is in use at both islands. O One hose is in use on one island. Compute the probability of this event. P(X= 0 and Y# 0) =
MATLAB: An Introduction with Applications
6th Edition
ISBN:9781119256830
Author:Amos Gilat
Publisher:Amos Gilat
Chapter1: Starting With Matlab
Section: Chapter Questions
Problem 1P
Related questions
Question
4a Answer pls a and b and c only
Transcribed Image Text:A service station has both self-service and full-service islands. On each island, there is a single regular unleaded pump with two hoses. Let X denote the number of hoses being used on the
self-service island at a particular time, and let y denote the number of hoses on the full-service island in use at that time. The joint pmf of X and Y appears in the accompanying tabulation.
p(x, y)
0
1
2
(a) What is P(X = 1 and Y = 1)?
P(X = 1 and Y = 1) = [
(b) Compute P(X ≤ 1 and Y ≤ 1).
P(X ≤ 1 and Y ≤ 1) = [
y
0
1 2
0.10 0.03 0.01
0.07 0.20 0.08
0.05 0.14 0.32
(c) Give a word description of the event {X = 0 and Y# 0}.
O At least one hose is in use at both islands.
One hose is in use on both islands.
At most one hose is in use at both islands.
O One hose is in use on one island.
Compute the probability of this event.
P(X = 0 and Y = 0) = [
y
Py(y)
(d) Compute the marginal pmf of X.
0
Px (x)
Compute the marginal pmf of Y.
0
Using P(x), what is P(X ≤ 1)?
P(X ≤ 1) =
1
1
(e) Are X and Y independent rv's? Explain.
2
2
O X and Y are not independent because P(x,y) = Px(x) - P₁(y).
O X and Y are not independent because P(x,y) = Px(x) - P₂(y).
O X and Y are independent because P(x,y) # Px(x) - P₂(y).
O X and Y are independent because P(x,y) = Px(x) - P₂(y).
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