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.
y | ||||
p(x, y) |
0 | 1 | 2 | |
x | 0 | 0.10 | 0.05 | 0.02 |
1 | 0.07 | 0.20 | 0.08 | |
2 | 0.05 | 0.14 | 0.29 |
(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)
=
Compute the probability of this event.
P(X ≠ 0 and Y ≠ 0) =
(d) Compute the marginal pmf of X.
x | 0 | 1 | 2 |
pX(x) |
Compute the marginal pmf of Y.
y | 0 | 1 | 2 |
pY(y) |
Using pX(x), what is
P(X ≤ 1)?
P(X ≤ 1) =
a.)P(X = 1 and Y = 1) =0.20
b.)P(X ≤ 1 and Y ≤ 1) =0.10+0.05+0.07+0.20=0.42
P(X ≠ 0 and Y ≠ 0) = 0.20+0.08+0.14+0.29=0.71
d.)
x | 0 | 1 | 2 |
pX(x) | 0.10+0.05+0.02=0.17 | 0.07+0.20+ 0.08=0.35 | 0.05+0.14+0.29= 0.48 |
y | 0 | 1 | 2 |
pY(y) | 0.10+0.07+0.05= 0.22 | 0.05+0.20+0.14=0.39 | 0.02+0.08+0.29= 0.39 |
P(X ≤ 1) = 0.17+0.35=0.52
A service station has both self-service and full-service islands. On each island, there is a single...
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 Plx, y) 0 1 2 0 0.10 0.07 0.05 1 0.04 0.20...
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. y p(x, y) 0 1 2 0 0.05 0.01 1 0.10 0.06...
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. y p(x, y) 0 1 2 x 0 0.10 0.03 0.01 1 ...
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 is the full-service island in use at that time. The joint pmf of X and Y appears in the accompanying tabulation У Р(x, у) 0 1 2. 0.10 0.05 0.01 1 0.06 0.20 0.06 X 2 0.05 0.14 0.33 (a) Given that X = 1, determine...
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 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. $$ \begin{array}{lc|ccc} & & & y & \\ p(x, y) & & 0 &...
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) у 0 1 0.06 0 0.03 X 2 0.01 0.09 0.11...
A service station has both selt-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 partioular time, and let dencte the number of hoses on the full-service island in use at that time. The jeintpX and Y appears in the accompanying tabulation. n.05 ǚ.14 0.29 (a) Given that X 1, determine the conditional pmf of y-i e ortx(01),...
explain as much as possible, thanks
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 0 y 1...
service sta: cr has both self-service and ful service islancs on each island, there is ฮ single opular uneeded pump et thet time The joint pmf uf X nd Y ppears in the ocumpanying tebulstion, (Give answers to 2 deomsl pleces) ith two hoses LetX derote the number cf hoses being used on the self-service islanc st pettua me, and let r dencte the number cr hcses on the full-serice Isl nd in use x,y) 0.20 0.14 (a: what is...
Please answer all rest questions. Thanks!
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) у 0 1 2 0...