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2 answers:
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Answer:
a) Joint ptobability distribution
b) P(X<= 1 and Y <= 1) = P(X<= 1) * P(Y<=1) = 0.56
c) P(X + Y = 0)=0.3
d) P(X + Y <= 1)=0.53
Step-by-step explanation:
We have to construct the joint probability table with the marginal probabilities of X and Y.
X can take values from 0 to 2, and Y can take values from 0 to 4.
We can calculate each point of the joint probability as:
Then, the joint probabilities are:
X=0 Y=0 Px=0.5 Px=0.6 P(0,0)=0.3
X=0 Y=1 Px=0.5 Px=0.1 P(0,1)=0.05
X=0 Y=2 Px=0.5 Px=0.05 P(0,2)=0.025
X=0 Y=3 Px=0.5 Px=0.05 P(0,3)=0.025
X=0 Y=4 Px=0.5 Px=0.2 P(0,4)=0.1
X=1 Y=0 Px=0.3 Px=0.6 P(1,0)=0.18
X=1 Y=1 Px=0.3 Px=0.1 P(1,1)=0.03
X=1 Y=2 Px=0.3 Px=0.05 P(1,2)=0.015
X=1 Y=3 Px=0.3 Px=0.05 P(1,3)=0.015
X=1 Y=4 Px=0.3 Px=0.2 P(1,4)=0.06
X=2 Y=0 Px=0.2 Px=0.6 P(2,0)=0.12
X=2 Y=1 Px=0.2 Px=0.1 P(2,1)=0.02
X=2 Y=2 Px=0.2 Px=0.05 P(2,2)=0.01
X=2 Y=3 Px=0.2 Px=0.05 P(2,3)=0.01
X=2 Y=4 Px=0.2 Px=0.2 P(2,4)=0.04
We can write it in the form of a matrix:
b) From the joint probability P(X<= 1 and Y <= 1) is equal to
We can calculate P(X<= 1) * P(Y<=1)
Both calculations give the same result.
c) Probability of no violations
d) P(X + Y <= 1)
Answer:
The standard error of the mean = 2
Step-by-step explanation:
Given that:
The standard deviation σ = 14
The sample size n = 49
The sample mean = 56
The formula for calculating the standard error can be expressed as:
S.E = 2
Therefore, the standard error of the mean = 2
Answer:
b) 9x² - 3x
Step-by-step explanation:
Area of a rectangle = Length × Width
Area for the rectangle = 3x - 1 × 3x
Area =
Step 1. Multiply by combining like terms
3x · 3x = 9x²
Step 2. Multiply -1 by 3x
-1 · 3x = -3x
Step 3. Combine 9x² and -3x
9x² - 3x
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