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BaLLatris [955]
3 years ago
15

Nicholas has $50 to use while he is on a vacation. He decides to spend $5

Mathematics
1 answer:
Likurg_2 [28]3 years ago
4 0

Answer:

days(d) = 50 ÷ 5

Explanation:

50 ÷ 5 =  number of days

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The sales tax in your city is 4.4%, and an item costs $3 before tax.
defon

Answer:

0.132

Step-by-step explanation:

4.4%*3=0.132

6 0
3 years ago
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
Remy bought a bottle of water with a volume of 0.56 L. After Remy drank some of the water there was 0.17 L left. How much water
Nadya [2.5K]

Answer:

0.73 L

Step-by-step explanation:

3 0
3 years ago
7<br> Solve the system of equations by<br> graphing.<br> y = 2x – 5<br> 2y - 4x = 4
STatiana [176]

Answer:

No solution

Step-by-step explanation:

the two lines are parallel on the graph, they never intersect

4 0
3 years ago
HELP ME PLEASE!!!!!!!!!!!​
maks197457 [2]

Answer:

y - 7 = 5/4(x - 3)

Hope that helps

8 0
2 years ago
Read 2 more answers
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