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3 years ago

HELPP URGENT!

Mathematics

2 answers:

ollegr [7]3 years ago

4 0

Answer:

Step-by-step explanation:

It’s B

bixtya [17]3 years ago

3 0

Answer:

Step-by-step explanation:

I had this question on a test and got it right

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Let X and Y be discrete random variables. Let E[X] and var[X] be the expected value and variance, respectively, of a random vari

Ulleksa [173]

Answer:

(a) $E[X+Y]=E[X]+E[Y]$

(b) $Var(X+Y)=Var(X)+Var(Y)$

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

$E[f(X,Y)]=\sum_{x,y}f(x,y)\cdot P(X=x, Y=y).$

Since f(X,Y)=X+Y

$E[X+Y]=\sum_{x,y}(x+y)P(X=x,Y=y)\\=\sum_{x,y}xP(X=x,Y=y)+\sum_{x,y}yP(X=x,Y=y).$

Let us look at the first of these sums.

$\sum_{x,y}xP(X=x,Y=y)\\=\sum_{x}x\sum_{y}P(X=x,Y=y)\\\text{Taking Marginal distribution of x}\\=\sum_{x}xP(X=x)=E[X].$

Similarly,

$\sum_{x,y}yP(X=x,Y=y)\\=\sum_{y}y\sum_{x}P(X=x,Y=y)\\\text{Taking Marginal distribution of y}\\=\sum_{y}yP(Y=y)=E[Y].$

Combining these two gives the formula:

$\sum_{x,y}xP(X=x,Y=y)+\sum_{x,y}yP(X=x,Y=y) =E(X)+E(Y)$

Therefore:

$E[X+Y]=E[X]+E[Y] \text{ as required.}$

(b)We want to show that if X and Y are independent random variables, then:

$Var(X+Y)=Var(X)+Var(Y)$

By definition of Variance, we have that:

$Var(X+Y)=E(X+Y-E[X+Y]^2)$

$=E[(X-\mu_X +Y- \mu_Y)^2]\\=E[(X-\mu_X)^2 +(Y- \mu_Y)^2+2(X-\mu_X)(Y- \mu_Y)]\\$Since we have shown that expectation is linear$\\=E(X-\mu_X)^2 +E(Y- \mu_Y)^2+2E(X-\mu_X)(Y- \mu_Y)]\\=E[(X-E(X)]^2 +E[Y- E(Y)]^2+2Cov (X,Y)$

Since X and Y are independent, Cov(X,Y)=0

$=Var(X)+Var(Y)$

Therefore as required:

$Var(X+Y)=Var(X)+Var(Y)$

7 0

3 years ago

Which of the following defines liquid measure?

Aleks04 [339]

B units used to measure the volume of liquids such as water gas and milk because the measure of the liquid is defined by the unit used

6 0

3 years ago

Dur rn help pls ))))))))))

Vadim26 [7]

Answer:

A is correct good luck bud

Step-by-step explanation:

3 0

2 years ago

An extraordinarily large fish was pulled in by a group of fishermen. It weighed 41 lbs and 8 oz. Find the fish’s weight in ounce

Virty [35]

Answer:

664

Step-by-step explanation:

41 lbs and 8 oz = 41.5 lbs bc 8 oz is half a lbs

so 41.5*16=664

3 0

3 years ago

1. Write down four different numbers with a median of 4.5

Arada [10]

Answer:

1. 3,4,5,6

Because if you were to do 3+4+5+6 Then divide by 4. You get 4.5.

2. -6 + (-4) + (-2) + 2 + 4 + 6

Gets you 0

Step-by-step explanation:

Sorry if this doesn't help.

8 0

3 years ago

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