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3 years ago

7

Suppose two random variables, X and Y are independent, which statement is false? a) P(X∣Y)=P(X) b) P(X∪Y)=P(X)+P(Y) c) P(X∩Y)=P(

X)⋅P(Y) d) Cov(X,Y)=0

1 answer:

Svetlanka [38]3 years ago

5 0

B is false, since by the inclusion/exclusion principle,

$P(X\cup Y)=P(X)+P(Y)-P(X\cap Y)$

By independence, we have $P(X\cap Y)=P(X)P(Y)$ , which is zero if either of $P(X)$ or $P(Y)$ is 0, which isn't guaranteed.

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I need help on number 10 , number 9 and number 11 thank you

Illusion [34]

9.
2(13-p)
2(13-2)=22
2(13-3)= 20
2(13-4)= 18
10.
3v+w
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3*8+4= 28
11. you cannot see enough to do the problem so what ever the problem is you take the numbers and replace x with them 2 for the first one= x then do the problem to get the answer.

4 0

3 years ago

What are the solutions of x^2-2x+5=0

sweet [91]

The solution of $x^{2}-2 x+5=0$ are 1 + 2i and 1 – 2i

<u>Solution:</u>

Given, equation is $x^{2}-2 x+5=0$

We have to find the roots of the given quadratic equation

Now, let us use the quadratic formula

$x=\frac{-b \pm \sqrt{b^{2}-4 a c}}{2 a}$ --- (1)

<em><u>Let us determine the nature of roots:</u></em>

Here in $x^{2}-2 x+5=0$ a = 1 ; b = -2 ; c = 5

$b^2 - 4ac = 2^2 - 4(1)(5) = 4 - 20 = -16$

Since $b^2 - 4ac < 0$ , the roots obtained will be complex conjugates.

Now plug in values in eqn 1, we get,

$x=\frac{-(-2) \pm \sqrt{(-2)^{2}-4 \times 1 \times 5}}{2 \times 1}$

On solving we get,

$x=\frac{2 \pm \sqrt{4-20}}{2}$

$x=\frac{2 \pm \sqrt{-16}}{2}$

$x=\frac{2 \pm \sqrt{16} \times \sqrt{-1}}{2}$

we know that square root of -1 is "i" which is a complex number

$\begin{array}{l}{\mathrm{x}=\frac{2 \pm 4 i}{2}} \\\\ {\mathrm{x}=1 \pm 2 i}\end{array}$

Hence, the roots of the given quadratic equation are 1 + 2i and 1 – 2i

6 0

3 years ago

Write an equivalent expression using the Distributive Property.

rusak2 [61]

Answer:

35 + 21 = 7(5 + 3)

Step-by-step explanation:

In this question, we have to write an equivalent expression to the one on the left, while using the distributive property.

Our equation is: 35 + 21 = 7(_ + _), we have to find the missing values.

In the equation, we can see that 7 is divisible to 35 and 21, which means we can simply divide in order to get our missing numbers.

Divide:

35/7 = 5

21/7 = 3

When we plug those values into our equation, it would be:

35 + 21 = 7(5 + 3)

When you use distributive property by distributing the 7 to the number inside the parenthesis, you would get this:

35 + 21 = 35 + 21

When you simplify, you would get the same answer.

56 = 56.

Therefore, your answer would be 35 + 21 = 7(5 + 3)

4 0

3 years ago

Read 2 more answers

The sets of numbers 3, 4, 5, and 8, 15, 17 are Pythagorean triples. Use what you know about the Pythagorean Theorem and explain

Leviafan [203]

Answer:

Pythagorean Theorom: a^2+b^2=c^2

Take the largest number of each as C (hypotenuse)

<u>3,4</u><u>,</u><u>5</u>

(3)^2+(4)^2= (5)^2

25=25

Therefore it is a Pythagorean Triple.

<u>8,15,17</u>

(8)^2+(15)^2=(17)^2

289=289

Therefore it is a Pythagorean Triple.

7 0

4 years ago

on a map of new mexieco 1cm represents 45km the distance from albuquerque to santa fe is 2cm find the actual distance I NEED HEL

cestrela7 [59]

You are told 1 cm = 45 km

The distance is 2cm

2cm / 1cm = 2

2 x 45 = 90 km

The distance is 90 km.

8 0

3 years ago