Answer:
48 cats
Step-by-step explanation:
Am interesting factoid about ratios:
The ratio can be separated into fractional parts of
and
. We need to know the cat part.
, so that is the fraction part. Then, we multiply this fraction by 168 to get the total number of cats. This number is 48.
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: