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2 years ago

PLEASE, PLEASE HELP !! :(

Mathematics

1 answer:

allochka39001 [22]2 years ago

5 0

Answer:

no association

Step-by-step explanation:

hope this helps I'm pretty sure this is 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

2 years ago

Need answer pls any of them

Vinvika [58]

Answer:

number 4. 13

because first you do the exponents giving you 8 and then divide which is 2 then you subtract which is 13

5 0

2 years ago

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Solve for x. -5(x – 4) = -30 Enter your answer in the box. x =

Svetlanka [38]

Answer:

$- 5(x - 4) = 30$

$- 5x + 20 = 30$

$- 5x = 30 - 20 = 10$

$x = 10 \div - 5$

$x = - 2$

3 0

2 years ago

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Evaluate the expression n-f x 8 if n= 84.15 and f=1.8

Gnesinka [82]

84.15-1.8*8
Order of Operations says to add and subtract before you multiply, so simplify the expression to: 82.35*8, which is 658.8

6 0

2 years ago

Rewrite Y=4-3x+x squared in standard form and correctly

Whitepunk [10]

Answer:

Step-by-step explanation:

y = 4 - 3x + x^2 is to be rewritten in standard form. To do this, rearrange the terms in order of powers of x, from highest to lowest.

y = 4 - 3x + x^2 becomes y = x^2 - 3x + 4

4 0

2 years ago