How do I solve number five and what is the answer?
2 answers:
keeping in mind that we can convert any value in percent format to a percent fraction by simply dividing it by 100, this one is 17.5, so let's first convert that 17.5 to a fraction, namely an improper fraction in this case, we have one decimal, .5, so we'll divide it by 10, and then we'll do the percent fraction conversion.
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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: