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kaheart [24]
3 years ago
8

In an arithmetic sequence, a3=15 and a8=0. What is the value of a5?

Mathematics
1 answer:
grin007 [14]3 years ago
6 0
The value of a5 is 9
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What expressions are equivalent to 4(4a+5)
Firlakuza [10]

Answer:

<h3>16a + 20</h3>

Step-by-step explanation:

4(4a + 5)         <em>use distributive property</em>

= (4)(4a) + (4)(5) = 16a + 20

5 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
Math homework due tomorrow
Margarita [4]
5.5-3b = 2b-6.25 5.5+6.25 = 2b+3b 11.75 = 5b 11.75/5 = 5b/5 2.35 = b
8 0
3 years ago
Which expression is equal to
Andreyy89
Please fix the equation in the second part. Is it + or -.
4 0
3 years ago
Read 2 more answers
determine the area of a trapezoid the length of the midline of 14 centimeters and the length of the height of 8 centimeters
emmainna [20.7K]

Answer:

Area = 112cm^2

Step-by-step explanation:

Area = (a + b)*h / 2

M = (a + b) / 2

14 = (a + b) /

2*14 = a + b

28 = a + b

Area = 28*8 / 2

Area = 112 cm^2

5 0
2 years ago
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