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defon
3 years ago
15

Suppose Q and R are independent events. Find P(Q and R) if P(Q) = 0.63 and P(R) = 0.48.

Mathematics
2 answers:
DENIUS [597]3 years ago
8 0

Answer:

Option B is correct

0.3024

Step-by-step explanation:

Definition:

If event A and B are independent, then;

P(A \cap B) = P(A) \cdot P(B)

Given that:

Suppose Q and R are independent events.

We have to find P(Q \cap R)

It is given that:

P(Q) = 0.63 and P(R) = 0.48

then by definition we have;

P(Q \cap R) = P(Q) \cdot P(R)

Substitute the given values we have;

P(Q \cap R) =0.63 \cdot 0.48

Simplify:

P(Q \cap R) =0.3024

Therefore, the value of P(Q \cap R) is 0.3024

Oksanka [162]3 years ago
5 0
Hello,

Q and R are independent if p(Q and R)=p(Q)*p(R)
Here p(Q and R)=0.63-0.48=0.3024
ANSWER B
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A circle has a diameter with endpoints at (6, 5) and (8, 5). Write the equation for the circle.
mario62 [17]

Answer:

(x-7)^2+(y-5)^2=1

Step-by-step explanation:

The two things that are required to formulate the equation of the circle is the center coordinate and the radius of the circle!

<u>Center of the circle:</u>

  • The center of the circle always lies at the midpoint of the endpoints of its diameter: Let's call the endpoints A(6,5) and B(8,5).

Using the midpoint formula we'll get:

(x_m, y_m) = \left(\dfrac{x_1+x_2}{2},\dfrac{y_1+y_2}{2}\right)

(x_m, y_m) = \left(\dfrac{6+8}{2},\dfrac{5+5}{2}\right)

(x_m, y_m) = (7,5)

This is the center coordinate of our circle.

<u>Radius: </u>

The radius of the circle is the distance from the center of the circle to any of the endpoints of the diameter (A or B)

We can use the distance formula:

r = \sqrt{(x_1-x_2)^2+(y_1-y_2)^2}

r = \sqrt{(x_1-x_m)^2+(y_1-y_m)^2}

r = \sqrt{(6-7)^2+(5-5)^2}

r = \sqrt{1^2}

r = 1

<u>Equation of the circle: </u>

The equation is written as:

(x-a)^2+(y-b)^2=r^2

here, (a,b) are the center points of the circle

in our case this is (a,b)=(x_m,y_m)=(7,5)

and r = 1

(x-7)^2+(y-5)^2=1^2

(x-7)^2+(y-5)^2=1

This is the equation of the circle!

3 0
3 years ago
henry and his brother each start a savings account. henry begins with $200 and deposits $25 each month. his brother begins with
zlopas [31]

Answer:

Henry after 2 months: 250

His brother after 2 months: 220

Step-by-step explanation:

Henry started with $200 so add $25 twice (for 2 months) and get $250 dollars after 2 months.

His brother started with $150 so add $35 twice and get $220 dollars after 2 months

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3 years ago
Which function has a greater y value if x=2<br> O<br> Blue<br> Red
LenaWriter [7]

Answer:

Guessing the answer should be the blue one because it is going up the graph steeper.

Step-by-step explanation:

4 0
3 years ago
a. esteban-perez and j. m. morales ´ , distributionally robust stochastic programs with side information based on trimmings, mat
sleet_krkn [62]

Distributionally robust stochastic programs with side information based on trimmings

This is a research paper whose authors are Adrián Esteban-Pérez and Juan M. Morales.

Abstract:

  • We look at stochastic programmes that are conditional on some covariate information, where the only knowledge of the possible relationship between the unknown parameters and the covariates is a limited data sample of their joint distribution. We build a data-driven Distributionally Robust Optimization (DRO) framework to hedge the decision against the inherent error in the process of inferring conditional information from limited joint data by leveraging the close relationship between the notion of trimmings of a probability measure and the partial mass transportation problem.
  • We demonstrate that our technique is computationally as tractable as the usual (no side information) Wasserstein-metric-based DRO and provides performance guarantees. Furthermore, our DRO framework may be easily applied to data-driven decision-making issues involving tainted samples. Finally, using a single-item newsvendor problem and a portfolio allocation problem with side information, the theoretical findings are presented.

Conclusions:

  • We used the relationship between probability reductions and partial mass transit in this study to give a straightforward, yet powerful and creative technique to expand the usual Wasserstein-metric-based DRO to the situation of conditional stochastic programming. In the process of inferring the conditional probability measure of the random parameters from a limited sample drawn from the genuine joint data-generating distribution, our technique generates judgments that are distributionally resilient to uncertainty. In a series of numerical tests based on the single-item newsvendor issue and a portfolio allocation problem, we proved that our strategy achieves much higher out-of-sample performance than several current options. We backed up these actual findings with theoretical analysis, demonstrating that our strategy had appealing performance guarantees.

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2 years ago
4, Find a number x such that x = 1 mod 4, x 2 mod 7, and x 5 mod 9.
olchik [2.2K]

4, 7 and 9 are mutually coprime, so you can use the Chinese remainder theorem.

Start with

x=7\cdot9+4\cdot2\cdot9+4\cdot7\cdot5

Taken mod 4, the last two terms vanish and we're left with

x\equiv63\equiv64-1\equiv-1\equiv3\pmod4

We have 3^2\equiv9\equiv1\pmod4, so we can multiply the first term by 3 to guarantee that we end up with 1 mod 4.

x=7\cdot9\cdot3+4\cdot2\cdot9+4\cdot7\cdot5

Taken mod 7, the first and last terms vanish and we're left with

x\equiv72\equiv2\pmod7

which is what we want, so no adjustments needed here.

x=7\cdot9\cdot3+4\cdot2\cdot9+4\cdot7\cdot5

Taken mod 9, the first two terms vanish and we're left with

x\equiv140\equiv5\pmod9

so we don't need to make any adjustments here, and we end up with x=401.

By the Chinese remainder theorem, we find that any x such that

x\equiv401\pmod{4\cdot7\cdot9}\implies x\equiv149\pmod{252}

is a solution to this system, i.e. x=149+252n for any integer n, the smallest and positive of which is 149.

3 0
3 years ago
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