All categories

2 years ago

Use the function below to find F(3).

Mathematics

1 answer:

pickupchik [31]2 years ago

7 0

Answer:

Step-by-step explanation:

If the function equation is F(x)=3x. You just plug in the 3 from F(3) in for the x.

F(x)= 3x

↓

F(3)=3(3)

F(3)=9

You might be interested in

it took Simon 33 minutes to run 5.5 miles. did he run faster or slower than 1 mile every 5 minutes how can you tell

vitfil [10]

Simon ran slower than 1 mile every 5 minutes.

Because 33 / 5.5 = 6. So he ran 1 mile every 6 minutes, not 5.

4 0

2 years ago

Which of the following statements about rational numbers is not correct? А All whole numbers are also rational numbers. B All ra

iren2701 [21]

Step-by-step explanation:

1736-8166x71662=8177103 :D

3 0

3 years ago

The odds against Carl beating his friend in a round of golf are 9:7. Find the probability that Carl will lose?

grandymaker [24]

The ratio 9:7 gives you following statement:

Carl will win in 9 cases from 9+7=16;
Carl will lose in 7 cases from 16.

Then the probability that Carl will lose is

$Pr(\text{Carl will lose})=\dfrac{7}{16}.$

Answer: $Pr(\text{Carl will lose})=\dfrac{7}{16}.$

7 0

3 years ago

Let $$X_1, X_2, ...X_n$$ be uniformly distributed on the interval 0 to a. Recall that the maximum likelihood estimator of a is $

Solnce55 [7]

Answer:

a) $\hat a = max(X_i)$

For this case the value for $\hat a$ is always smaller than the value of a, assuming $X_i \sim Unif[0,a]$ So then for this case it cannot be unbiased because an unbiased estimator satisfy this property:

$E(a) - a= 0$ and that's not our case.

b) $E(\hat a) - a= \frac{na}{n+1} - a = \frac{na -an -a}{n+1}= \frac{-a}{n+1}$

Since is a negative value we can conclude that underestimate the real value a.

$\lim_{ n \to\infty} -\frac{1}{n+1}= 0$

c) $P(Y \leq y) = P(max(X_i) \leq y) = P(X_1 \leq y, X_2 \leq y, ..., X_n\leq y)$

And assuming independence we have this:

$P(Y \leq y) = P(X_1 \leq y) P(X_2 \leq y) .... P(X_n \leq y) = [P(X_1 \leq y)]^n = (\frac{y}{a})^n$

$f_Y (Y) = n (\frac{y}{a})^{n-1} * \frac{1}{a}= \frac{n}{a^n} y^{n-1} , y \in [0,a]$

e) On this case we see that the estimator $\hat a_1$ is better than $\hat a_2$ and the reason why is because:

$V(\hat a_1) > V(\hat a_2)$

$\frac{a^2}{3n}> \frac{a^2}{n(n+2)}$

$n(n+2) = n^2 + 2n > n +2n = 3n$ and that's satisfied for n>1.

Step-by-step explanation:

Part a

For this case we are assuming $X_1, X_2 , ..., X_n \sim U(0,a)$

And we are are ssuming the following estimator:

$\hat a = max(X_i)$

$E(a) - a= 0$ and that's not our case.

Part b

For this case we assume that the estimator is given by:

$E(\hat a) = \frac{na}{n+1}$

And using the definition of bias we have this:

$E(\hat a) - a= \frac{na}{n+1} - a = \frac{na -an -a}{n+1}= \frac{-a}{n+1}$

Since is a negative value we can conclude that underestimate the real value a.

And when we take the limit when n tend to infinity we got that the bias tend to 0.

$\lim_{ n \to\infty} -\frac{1}{n+1}= 0$

Part c

For this case we the followng random variable $Y = max (X_i)$ and we can find the cumulative distribution function like this:

$P(Y \leq y) = P(max(X_i) \leq y) = P(X_1 \leq y, X_2 \leq y, ..., X_n\leq y)$

And assuming independence we have this:

$P(Y \leq y) = P(X_1 \leq y) P(X_2 \leq y) .... P(X_n \leq y) = [P(X_1 \leq y)]^n = (\frac{y}{a})^n$

Since all the random variables have the same distribution.

Now we can find the density function derivating the distribution function like this:

$f_Y (Y) = n (\frac{y}{a})^{n-1} * \frac{1}{a}= \frac{n}{a^n} y^{n-1} , y \in [0,a]$

Now we can find the expected value for the random variable Y and we got this:

$E(Y) = \int_{0}^a \frac{n}{a^n} y^n dy = \frac{n}{a^n} \frac{a^{n+1}}{n+1}= \frac{an}{n+1}$

And the bias is given by:

$E(Y)-a=\frac{an}{n+1} -a=\frac{an-an-a}{n+1}= -\frac{a}{n+1}$

And again since the bias is not 0 we have a biased estimator.

Part e

For this case we have two estimators with the following variances:

$V(\hat a_1) = \frac{a^2}{3n}$

$V(\hat a_2) = \frac{a^2}{n(n+2)}$

On this case we see that the estimator $\hat a_1$ is better than $\hat a_2$ and the reason why is because:

$V(\hat a_1) > V(\hat a_2)$

$\frac{a^2}{3n}> \frac{a^2}{n(n+2)}$

$n(n+2) = n^2 + 2n > n +2n = 3n$ and that's satisfied for n>1.

8 0

3 years ago

Use implicit differentiation to find the negative slope of a tangent to the circle x^2+y^2=16 at x=-2

SVETLANKA909090 [29]

Answer:

slope = - $\frac{\sqrt{3} }{3}$

Step-by-step explanation:

Differentiating implicitly with respect to x

2x + 2y $\frac{dy}{dx}$ = 0

2y $\frac{dy}{dx}$ = - 2x

$\frac{dy}{dx}$ = - $\frac{2x}{2y}$ = - $\frac{x}{y}$

$\frac{dy}{dx}$ is the measure of the slope of the tangent

rearrange equation to find corresponding y-coordinate of x = - 2

y² = 16 - 4 = 12 = 2 $\sqrt{3}$ ⇒ y = ± 2 $\sqrt{3}$

using x = - 2, y = - 2 $\sqrt{3}$ , then

$\frac{dy}{dx}$ = - $\frac{1}{\sqrt{3} }$ = - $\frac{\sqrt{3} }{3}$

3 0

3 years ago