MATHEMATICS COLLEGE

M1Q11.) What percent of women in their 40s taking a screening mammography receive a false positive?

Answers

Answer 1

Answer:

Answer:

Answer 4. Because there is a 1/10th(0.1) of 0.9851 to receive a false positive.

0.9851×0.1×100=9.851%

is approximately equal to 10%

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Answers

Answer:

200

Step-by-step explanation:

Answer:

ITS C 200

Step-by-step explanation:

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.

Learn more about the Expected Value of Random Variables here:

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Answer:

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Please help me answer this In a game of chance, Scott can win in two different ways. One way is by rolling either a 1 or a 3 with a standard die. The second way is to land on a 4, 5, or 7 on the spinner with eight equally likely sections numbered from one to eight. Scott thinks he has a better chance with the spinner because he has three numbers that will win instead of only two. Is he correct? What is the probability of winning with the die? What is the probability of winning with the spinner? Which should he choose? Thank you if you are answering this is very hard

Answers

He is correct.The probability of winning with the die is while the probability of winning with the spinner is which is 0.375, slightly bigger than rolling the die!

Answer:

Step-by-step explanation:

By 12 the ansewr is 1000%

A soccer player scored 12 goals this season. He scored 30% of the goals for his team this season. How many goals did the entire team score this season?

Answers

Answer:

40 goalas

Step-by-step explanation:

30% x ? = 12

12/30% =

12/(30/100) =

(100 x 12)/30 =

1,200/30 =

The table shows the number of badges earned, based on the number of boxes of cards sold. What does b(20) = 3 mean in terms of the problem

Answers

Answer:

Someone who sells 20 boxes of cards earn 3 badges.

Step-by-step explanation:

Answer:

b(20) = 3 means that for 20 boxes of cards sold, 3 badges were earned.

Step-by-step explanation:

The number of badges earned based on the number of boxes of cards sold means that badges earned are a function of the number of boxes of cards sold.

b(20) means the number of badges earned for selling 20 boxes of cards.

b(20) = 3 means that for 20 boxes of cards sold, 3 badges were earned.

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