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andrezito [222]
2 years ago
7

A continuous random variable X has cdf F(x)=x² b (a) Determine the constants a and b. for a < 0, for 0 < x < 1, for x &

gt; 1.​

Mathematics
1 answer:
Karolina [17]2 years ago
8 0

Any proper CDF F(x) has the properties

• \displaystyle \lim_{x\to-\infty} F(x) = 0

• \displaystyle \lim_{x\to+\infty} F(x) = 1

so we have to have a = 0 and b = 1.

This follows from the definitions of PDFs and CDFs. The PDF must satisfy

\displaystyle \int_{-\infty}^\infty f(x) \, dx = 1

and so

\displaystyle \lim_{x\to-\infty} F(x) = \int_{-\infty}^{-\infty} f(t) \, dt = 0 \implies a = 0

\displaystyle \lim_{x\to+\infty} F(x) = \int_{-\infty}^\infty f(t) \, dt = 1 \implies b = 1

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dexar [7]

Answer:

P(A∩B) = 0.522

Step-by-step explanation:

Let's call A the event that a puppy is adopted and B the probability that a puppy live 7 or more years

So, the probability P(A∩B) that a randomly selected puppy in the shelter will get adopted and live 7 or more years is:

P(A∩B) = P(A)*P(B/A)

Because A and B are not independents.

Then, the probability P(A) that a puppy is adopted is 58% and the probability P(B/A) that a puppy live 7 or more years given that the puppy is adopted is 90%.

Finally, replacing the values, we get:

P(A∩B) = 0.58*0.9 = 0.522

It means that the 52.2% of the puppies are adopted and live 7 or more years.

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A rectangular prism is 7 centimeters long, 5 centimeters wide, and 4 centimeters tall. Which values are the areas of cross secti
VladimirAG [237]
Cross section is the area you make when you make a cut across a shape. In this case, the cut must be parallel to the base. Hence, the cut shape would be same to that of the base. The base's dimensions are 7 cm long x 5 cm wide. Thus, the cross section area is 35 square centimeters.
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Answer and Step-by-step explanation:

When trying to figure this out, we know that the numbers have to be one after the other, like 1, 2, 3, 4, or 55. 56, 57, 58. The last digit in the numbers also have to add to 6.

<u>The answer is:</u>

100 + 101 + 102 + 103

It adds up to 406, and the integers are consecutive.

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Answer:

9

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