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3 years ago

Y+2 y+2 y+2 y+2 y+2 ^ 30

Mathematics

2 answers:

LUCKY_DIMON [66]3 years ago

8 0

9y+1073741824

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BartSMP [9]3 years ago

5 0

Answer:

Step-by-step explanation:

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Canadians who visit the United States often buy liquor and cigarettes, which are much cheaper in the United States. However, the

fenix001 [56]

Answer:

(a): Marginal pmf of x

$P(0) = 0.72$

$P(1) = 0.28$

(b): Marginal pmf of y

$P(0) = 0.81$

$P(1) = 0.19$

(c): Mean and Variance of x

$E(x) = 0.28$

$Var(x) = 0.2016$

(d): Mean and Variance of y

$E(y) = 0.19$

$Var(y) = 0.1539$

(e): The covariance and the coefficient of correlation

$Cov(x,y) = 0.0468$

$r \approx 0.2657$

Step-by-step explanation:

Given

x = bottles

y = carton

See attachment for complete question

Solving (a): Marginal pmf of x

This is calculated as:

$P(x) = \sum\limits^{}_y\ P(x,y)$

So:

$P(0) = P(0,0) + P(0,1)$

$P(0) = 0.63 + 0.09$

$P(0) = 0.72$

$P(1) = P(1,0) + P(1,1)$

$P(1) = 0.18 + 0.10$

$P(1) = 0.28$

Solving (b): Marginal pmf of y

This is calculated as:

$P(y) = \sum\limits^{}_x\ P(x,y)$

So:

$P(0) = P(0,0) + P(1,0)$

$P(0) = 0.63 + 0.18$

$P(0) = 0.81$

$P(1) = P(0,1) + P(1,1)$

$P(1) = 0.09 + 0.10$

$P(1) = 0.19$

Solving (c): Mean and Variance of x

Mean is calculated as:

$E(x) = \sum( x * P(x))$

So, we have:

$E(x) = 0 * P(0) + 1 * P(1)$

$E(x) = 0 * 0.72 + 1 * 0.28$

$E(x) = 0 + 0.28$

$E(x) = 0.28$

Variance is calculated as:

$Var(x) = E(x^2) - (E(x))^2$

Calculate $E(x^2)$

$E(x^2) = \sum( x^2 * P(x))$

$E(x^2) = 0^2 * 0.72 + 1^2 * 0.28$

$E(x^2) = 0 + 0.28$

$E(x^2) = 0.28$

So:

$Var(x) = E(x^2) - (E(x))^2$

$Var(x) = 0.28 - 0.28^2$

$Var(x) = 0.28 - 0.0784$

$Var(x) = 0.2016$

Solving (d): Mean and Variance of y

Mean is calculated as:

$E(y) = \sum(y * P(y))$

So, we have:

$E(y) = 0 * P(0) + 1 * P(1)$

$E(y) = 0 * 0.81 + 1 * 0.19$

$E(y) = 0+0.19$

$E(y) = 0.19$

Variance is calculated as:

$Var(y) = E(y^2) - (E(y))^2$

Calculate $E(y^2)$

$E(y^2) = \sum(y^2 * P(y))$

$E(y^2) = 0^2 * 0.81 + 1^2 * 0.19$

$E(y^2) = 0 + 0.19$

$E(y^2) = 0.19$

So:

$Var(y) = E(y^2) - (E(y))^2$

$Var(y) = 0.19 - 0.19^2$

$Var(y) = 0.19 - 0.0361$

$Var(y) = 0.1539$

Solving (e): The covariance and the coefficient of correlation

Covariance is calculated as:

$COV(x,y) = E(xy) - E(x) * E(y)$

Calculate E(xy)

$E(xy) = \sum (xy * P(xy))$

This gives:

$E(xy) = x_0y_0 * P(0,0) + x_1y_0 * P(1,0) +x_0y_1 * P(0,1) + x_1y_1 * P(1,1)$

$E(xy) = 0*0 * 0.63 + 1*0 * 0.18 +0*1 * 0.09 + 1*1 * 0.1$

$E(xy) = 0+0+0 + 0.1$

$E(xy) = 0.1$

So:

$COV(x,y) = E(xy) - E(x) * E(y)$

$Cov(x,y) = 0.1 - 0.28 * 0.19$

$Cov(x,y) = 0.1 - 0.0532$

$Cov(x,y) = 0.0468$

The coefficient of correlation is then calculated as:

$r = \frac{Cov(x,y)}{\sqrt{Var(x) * Var(y)}}$

$r = \frac{0.0468}{\sqrt{0.2016 * 0.1539}}$

$r = \frac{0.0468}{\sqrt{0.03102624}}$

$r = \frac{0.0468}{0.17614266944}$

$r = 0.26569371378$

$r \approx 0.2657$ --- approximated

8 0

3 years ago

3. How many solutions does the equation have?

Pepsi [2]

An infinite number of solutions since the right side is equal the left side for every value of x.

3 0

2 years ago

You are standing 30 meters from a hot air balloon that is preparing to take

Lerok [7]

Answer:

The distance to the top of the balloon is approximately 33.977 meters

Step-by-step explanation:

The (horizontal) distance from the hot air balloon from the observer, l = 30 m

The angle of elevation to the top of the balloon, θ = 28°

With the balloon standing upright, the distance to the top of the balloon, d, the height of the balloon, h and the horizontal distance to the balloon, l, form a right triangle, where;

d = The hypotenuse side

l = The leg adjacent to the reference (given) angle,

h = The leg opposite to the given angle, θ

By trigonometric ratios, we have;

$cos\angle X = \dfrac{Adjacent\ leg \ length}{Hypotenuse \ length}$

From which we get;

$cos\angle \theta = \dfrac{l}{d}$

$cos(28^{\circ}) = \dfrac{30 \ m}{d}$

$d = \dfrac{30 \ m}{cos(28^{\circ}) } \approx 33.977 \, m$

The distance to the top of the balloon, d ≈ 33.977 m

8 0

3 years ago

Draw 4 non collinear points

harina [27]

I don't know if you have to do this on a graph, or just on a blank space. But, noncollinear means, "not on the same line". So, if you were to draw four points in a blank spot on a piece of paper, just draw four points in random places, making sure they aren't all directly in line with eachother. For a graph, use points like: (-6,2), (5,7), (8,3), and (1,-3). Notice that none of them have the same x or y coordinates, so they can't possibly be collinear.

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3 years ago

A box of colored pencils contains exactly 6 red pencils. The probability of choosing a red pencil from the box is 2/7. How many

ZanzabumX [31]

Answer:

B.21

Step-by-step explanation:

Calculator

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3 years ago