Answer:
c = 0.165
Step-by-step explanation:
Given:
f(x, y) = cx y(1 + y) for 0 ≤ x ≤ 3 and 0 ≤ y ≤ 3,
f(x, y) = 0 otherwise.
Required:
The value of c
To find the value of c, we make use of the property of a joint probability distribution function which states that
where a and b represent -infinity to +infinity (in other words, the bound of the distribution)
By substituting cx y(1 + y) for f(x, y) and replacing a and b with their respective values, we have
Since c is a constant, we can bring it out of the integral sign; to give us
Open the bracket
Integrate with respect to y
Substitute 0 and 3 for y
Add fraction
Rewrite;
The is a constant, so it can be removed from the integral sign to give
Integrate with respect to x
Substitute 0 and 3 for x
Multiply both sides by
Answer:
B [2,∞)
Step-by-step explanation:
Given:
Current population = x
The population of a city is expected to decrease by 6% next year.
To find:
The expression that represents the expected population next year.
Solution:
We have,
Current population = x
Decrease rate = 6%.
Expected population next year = Current population - 6% of Current population
=
=
=
Therefore, the expression for the expected population next year is 0.94x.
X=3. Y=2
2=1+3. No. 2 does not equal 4