(x - 10)² is the graph x² by translation of 10 units moved to the right.
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:
180 degrees
Step-by-step explanation:
Two angles are supplementary when they add up to 180 degrees. Therefore, the sum of Angle L and M's measures is equal to 180°.
Answer:
Step-by-step explanation:
twice the difference of a number and 3 is added to 4
Answer: Any equation that has a -5 before the x will have the same slope. Some examples could be:
y= -5x
y = -5x + 100
y = -5x - 3