Decide whether the following situation is looking for the percent, the part, or the whole:The 14 compact cars sold by a dealer o
1 answer:
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Answer:
(a)
(b)
Step-by-step explanation:
Let X and Y be discrete random variables and E(X) and Var(X) are the Expected Values and Variance of X respectively.
(a)We want to show that E[X + Y ] = E[X] + E[Y ].
When we have two random variables instead of one, we consider their joint distribution function.
For a function f(X,Y) of discrete variables X and Y, we can define
Since f(X,Y)=X+Y
Let us look at the first of these sums.
Similarly,
Combining these two gives the formula:
Therefore:
(b)We want to show that if X and Y are independent random variables, then:
By definition of Variance, we have that:
Since X and Y are independent, Cov(X,Y)=0
Therefore as required:
Answer:
Approximately 42 times larger
Step-by-step explanation:
The diameter of a sphere is 2,160 mm.
The diameter of a second sphere is 7,520 mm.
To see how many times larger is the diameter of second sphere is than the diameter of the second sphere, we divide to get:
To see how many times larger the volume is, we cube both sides
This implies that
Therefore the volume of the second sphere is approximately 42 times larger