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Can someone pls help with this question :)

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Answer 1

Answer:

Answer:

Step by step

Step-by-step explanation:

I need points lol

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If x1, x2, . . . , xn are independent and identically distributed random variables having uniform distributions over (0, 1), find (a) e[max(x1, . . . , xn)]; (b) e[min(x1, . . . , xn)].

Answers

Denote by $X_((n))$ the maximum order statistic, with $X_((n))=\max\{X_1,\ldots,X_n\}$ , and similarly denote by $X_((1))$ the minimum order statistic. Then the CDF for $X_((n))$ is

$F_{X_((n))}(x)=\mathbb P(X_((n))\le x)$

In order for there to be some $x$ that exceeds the value of $X_((n))$ , it must be true that $x$ exceeds the value of all the $X_i$ , so the above is equivalent to the joint probability

$F_{X_((n))}(x)=\mathbb P(X_1\le x,\ldots,X_n\le x)$

and since the $X_i$ are i.i.d., we have

$F_{X_((n))}(x)=\mathbb P(X_1\le x)\cdots\mathbb P(X_n\le x)=\mathbb P(X_1\le x)^n$
$\implies F_{X_((n))}(x)=F_X(x)^n$

where $X\sim\mathrm{Unif}(0,1)$ . We have

$F_X(x)=\begin{cases}0&\text{for }x<0\nx&\text{for }0\le x\le1\n1&\text{for }x>1\end{cases}$

and so

$F_{X_((n))}(x)=\begin{cases}0&\text{for }x<0\nx^n&\text{for }0\le x\le1\n1&\text{for }x>1\end{cases}$
$\implies f_{X_((n))}(x)=\begin{cases}nx^(n-1)&\text{for }0<x<1\n0&\text{otherwise}\end{cases}$
$\implies\mathbb E[X_((n))]=\displaystyle\int_0^1xnx^(n-1)\,\mathrm dx=n\int_0^1x^n\,\mathrm dx=\frac n{n+1}$

Using similar reasoning, we can find the CDF for $X_((1))$ . We have

$F_{X_((1))}(x)=\mathbb P(X_((1))\le x)=1-\mathbb P(X_((1))>x)$
$F_{X_((1))}(x)=1-\mathbb P(X_1>x,\ldots,X_n>x)=1-\mathbb P(X_1>x)^n$
$F_{X_((1))}(x)=1-(1-\mathbb P(X\le x))^n=1-(1-F_X(x))^n$
$\implies F_{X_((1))}(x)=\begin{cases}0&\text{for }x<0\n1-(1-x)^n&\text{for }0\le x\le1\n1&\text{for }x>1\end{cases}$
$\implies f_{X_((1))}(x)=\begin{cases}n(1-x)^(n-1)&\text{for }0<x<1\n0&\text{otherwise}\end{cases}$
$\implies\mathbb E[X_((1))]=\displaystyle\int_0^1xn(1-x)^(n-1)\,\mathrm dx=\frac1{n+1}$

Final answer:

The expected values of the maximum and minimum of independent and identically distributed (iid) uniform random variables, x1, x2, ..., xn, are given by E[max(x1, ..., xn)] = n / (n + 1) and E[min(x1, ..., xn)] = 1 / (n + 1) respectively.

Explanation:

In mathematics, particularly in probability theory and statistics, the question is related to independent and identically distributed (iid) random variables with a uniform distribution. The expected value or mean (E) of the maximum (max) and minimum (min) of these random variables is sought.

(a) The expected value of the max of 'n' iid uniform random variables, x1, x2, ..., xn, is calculated by integrating the nth power of x from 0 to 1. It can be found via the equation E[max(x1, ..., xn)] = n / (n + 1).

(b) Similarly, the expected value of the min of 'n' iid uniform random variables is acquired by doing (1 / (n + 1)). Hence, E[min(x1, ..., xn)] = 1 / (n + 1).

By understanding these, you could visualize the various outcomes of the random variables and their distributions, demonstrating how likely each outcome could occur.

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CE is an angle bisector of angle ACB.If m angle ACE = 2x - 15 and m angle ECB = x +5,
determine the value of x.

Answers

The value of x from the angle bisector is: x = 20

How to find the value of the angle bisector?

Angle bisector theorem is a theorem in geometry that states that an angle bisector of a triangle divides the opposite side into two segments that are proportional to the other two sides of the triangle. An angle bisector is a ray that divides a given angle into two angles of equal measures.

Thus, we can say that:

∠ECB = ∠ACE

Thus:

x + 5 = 2x - 15

2x - x = 15 + 5

x = 20

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Answer:

x = 20

Step-by-step explanation:

$\because \overrightarrow {CE}$ is an angle bisector of $\angle ACB.$

$\therefore m \angle ACE = m \angle ECB\n 2x - 15 = x + 5 \n 2x - x = 15 + 5 \n \huge \orange{ x = 20}$

A rectangle has vertices (−5, 6), (−1, 6), (−1, 3), and (−5, 3). It is first dilated by the rule (x, y)→(7x, 7y) and then translated 10 units down. What are the coordinates of the image?A(−35, 32), (−7, 32), (−7, 11), (−35, 11)

B(−45, 42), (−17, 42), (−17, 21), (−45, 21)

C(−105, 42), (−77, 42), (−77, 21), (−105, 21)

D(−35,−28), (−7,−28), (−7,−49), (−35,−49)

Answers

Final answer:

By first dilating and then translating the given coordinates of the rectangle, we obtain the final coordinates as (−35, 32), (−7, 32), (−7, 11), (−35, 11). The correct answer is A.

Explanation:

The process of dilation involves multiplying the x and y coordinates of each vertex of the rectangle by a certain factor. In this case the factor is 7, which gives us the following set of coordinates after dilation: (−35, 42), (−7, 42), (−7, 21), (−35, 21). After the dilation, the rectangle is then translated down 10 units, which involves subtracting 10 from each of the y-coordinates. Following the translation, the final set of coordinates of the rectangle is (−35, 32), (−7, 32), (−7, 11), (−35, 11). Therefore, the correct answer is A.

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I think the answer is c

Will give extra points and brainliest !! /:

Answers

-1 +- sqrt (1^2 -4(2)(-4))

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2(2)

-1 +- sqrt(1+32)

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-1 +-sqrt(33)

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What’s d? I can’t see it

I need help plz and fast

Answers

Answer:

Step-by-step explanation:

1+19=20

so only 1 visit is available if they only have $20 to use.

Answer:

Step-by-step explanation:

19+1=20

The graph below represents a rock climbers height as she acends a hill. Part A- The above graph is (circle one) linear/ nonlinear. Part B- Is the above graph a function? Explain.

Answers

Answer:

Part A: its linear

Part B: it is a function

Step-by-step explanation:

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I need help! Please include an explanation.

Consider random samples of size 40 from a population with proportion 0.15. (a) Find the standard error of the distribution of sample proportions. Round your answer for the standard error to three decimal places.mean=______ standard error=_______ (b) Is the sample size large enough for the Central Limit Theorem to apply? 1. Yes 2. No