15 less than twice a number is less than or equal to -23. Into an equation

. Let X and Y be random variables of possible percent returns (0%, 10%,

bazaltina [42]

(a) The marginal distribution of X is

Pr(X = x) = ∑ Pr(X = x, Y = y)

… = 0.0625 + 0.0625 + 0.0625 + 0.0625

… = 0.25

That is, the first equality follows from the law of total probability, with the sum taken over y from {0, 5, 10, 15}. Each probability Pr(X = x, Y = y) is given in the table to be 0.0625.

Similarly, the marginal distribution of Y is

Pr(Y = y) = 0.25

(b) Yes, they're independent because

Pr(X = x, Y = y) = 0.0625,

and

Pr(X = x) Pr(Y = y) = 0.25 • 0.25 = 0.0625.

(c) The mean of X is

E[X] = ∑ x Pr(X = x)

… = 0.25 ∑ x

… = 0.25 (0 + 5 + 10 + 15)

… = 7.5

and you would find the same mean for Y,

E[Y] = 7.5

The variance of X is

V[X] = E[X^2] - E[X]^2

… = (∑ x^2 Pr(X = x)) - 7.5^2

… = 0.25 (∑ x^2) - 56.25

… = 0.25 (0^2 + 5^2 + 10^2 + 15^2) - 56.25

… = 31.25

and similarly,

V[Y] = 31.25

(each sum is taken with x and y from {0, 5, 10, 15})

7 0

3 years ago

Identify the probability to the nearest hundredth that a point chosen randomly inside the rectangle is in the triangle. HELP PLE

sashaice [31]

Answer:

$0.02$

Step-by-step explanation:

we know that

The probability that a point chosen randomly inside the rectangle is in the triangle is equal to divide the area of the triangle by the area of rectangle

Let

x-----> the area of triangle

y----> the area of rectangle

P -----> the probability

$P=x/y$

Find the area of triangle (x)

$A=(1/2)(5)(2)=5\ in^{2}$

Find the area of rectangle (y)

$A=18*12=216\ in^{2}$

Find the probability P

$P=5/216=0.02$

5 0

3 years ago

I NEED HELP PLEASE ...ASAP!!!!!

attashe74 [19]

-a²-3b³+c²+2b³-c²

= -(3)² - (3×2)³ + (-3)² + (2 × 2)³ - ( -3)²

= 9 - 24 + 9 + 16 - 9

= 1

answer is 1.

5 0

3 years ago

Ax+z=aw-y solve for a. show work please

dusya [7]

So the question is asking to covert the said formula by making the a as the solution or the ask of the said equation, well in that matter, I would say, base on my own conversion and further computation about the said equation, the value of a is (y+z)/(x+w). I hope this would help

5 0

3 years ago

Help me please giving brainiest

Setler79 [48]

Answer:

1) The most common place (mode) for people to jog is the path.

2) (The picture)

Step-by-step explanation:

1) The mode means what is most common, and since the path has 22 people, it is the most common place.

2) The data is distributed into 5 different columns based on how many people use the certain column. The second column is the mode and most common spot to jog.

4 0

2 years ago