Function

Problem 10201

Determine if the car is moving left or right at $t=8$ for the function $s(t)=-4 t^{3}-10 t^{2}+t-4$ .

See Solution

Problem 10202

Find the acceleration function $a(t)$ for the particle with position $s(t)=-3t^{2}-t+1$ (in meters) at time $t$ .

See Solution

Problem 10203

Find the acceleration of the particle at $t=3$ seconds for the function $s(t)=t^{3}-3 t^{2}-8 t+1$ . Answer in $\mathrm{ft} / \mathrm{s}^{2}$ .

See Solution

Problem 10204

Determine if the train, described by $s(t)=t^{4}-2 t^{3}-5 t^{2}+3$ , is speeding up or slowing down at $t=2$ seconds.

See Solution

Problem 10205

Find the interval(s) where the hummingbird slows down for $s(t)=-t^{3}+9 t^{2}-24 t-4$ , $t \geq 0$ .

See Solution

Problem 10206

Graph the function $f(x)=|x+4|-4$ and identify its domain and range.

See Solution

Problem 10207

A potato is shot up with a speed of $34 \mathrm{ft/s}$ from a 15 ft tall building. Find how long it's in the air using $s(t)=-16 t^{2}+34 t+15$ .

See Solution

Problem 10208

Question: Poisson Distribution
Let $X_{1}, X_{2}, \ldots, X_{n}$ be independent and identically distributed (i.i.d.) random variables, where each $X_{i}$ follows a Poisson distribution with parameter $\lambda>0$ . The probability mass function (PMF) for a Poisson random variable is given by:
Likelihood Estimation fo $f_{X}(x ; \lambda)=\frac{\lambda^{x} e^{-\lambda}}{x!}, \quad x=0,1,2, \ldots$ where $\lambda$ is the rate parameter of the Poisson distribution. (a) Write the likelihood function $L(\lambda)$ for the sample $X_{1}, X_{2}, \ldots, X_{n}$ . (b) Derive the log-likelihood function $\ell(\lambda)=\ln L(\lambda)$ . (c) Find the Maximum Likelihood Estimator (MLE) for $\lambda$ by solving $\frac{\partial e(\lambda)}{\partial \lambda}=$ 0 . (d) Verify that the second derivative of the log-likelihood function at the MLE is negative, confirming that the MLE is indeed a maximum. (e) Find the Fisher information for $\lambda, I(\lambda)=-E\left[\frac{\partial^{2} \ell(\lambda)}{\partial \lambda^{2}}\right]$ . (f) Using the MLE and Fisher information, calculate the Cramer-Rao lower bound for the variance of the MLE.

See Solution

Problem 10209

The mgf of a random variable $X$ is given by $m(t)=\left(0,9+0.1 e^{t}\right)^{3}$ , then $p(X=1)$ is equal to a. 0.0243 b. 0.536 c. 0.027 d. 0.725 e. 0.9

See Solution

Problem 10210

Marked out of 1.00
The moment generating function of a random variable X is given by $m(t)=0.3 e^{-t}+0.4+0.3 e^{2 t}$ . Then the mean of X is given by a. 0.4 b. 0.3 c. 0.9 d. 1 e. 2.4

See Solution

Problem 10211

Find the interval(s) where the car moves left for $s(t)=-t^{3}+6 t^{2}+36 t+4$ with $t \geq 0$ .

See Solution

Problem 10212

Find the ball's velocity when it first reaches $880 \mathrm{ft}$ , given $s(t)=-16 t^{2}+256 t$ .

See Solution

Problem 10213

$f(x)=x e^{x}-x$ is concave up ou?

See Solution

Problem 10214

8. If $f(x)=\left\{x^{2}+3\right.$ (A) $a=1, b=3$ (B) $\frac{1}{7}$ (C) $\frac{1}{3}$ (D) $\frac{1}{3}$ (B) $\left.a=\begin{array}{c}x<0 \\ 3, b=0\end{array}\right\}$ and $f(x)$ is differentiable at $x=0$ , then: (C) $a=3, b=1$ (D) $a=0, b=3$ $\begin{array}{lll}\text { (A) } x=\ln 2 & \text { (B) } x=\ln 5 & \text { (C) } x=\ln 3\end{array}$ (D) $x=2 \ln 5$

See Solution

Problem 10215

- A është vlerësues i pazhvendosur? Pse? 5.24. Shqyrtojmë shpërndarjen eksponenciale të zhvendosur me densitet $f(x)=\lambda e^{-\lambda(x-s)}$ $k u X \geq 5$ . Gjeni me anë të metodës së përgjasisë maksimale një vlerësues për $\lambda$ ?

See Solution

Problem 10216

B) If the function $f(x)=a x^{3}-3 x^{2}+b x+c$ has a local minimum at -5 and a local maximum at $x=\frac{-1}{2}$ and inflection point at $x=\frac{1}{4}$ find $a, b, c \in R$ .

See Solution

Problem 10217

Q3: A) Let M be a point moving on the curve $y^{2}=x^{3}$ such that rate of change the point $M$ getting away from of the origin point is 4 unit $/ \mathrm{s}$ . Find the rate of chang of the x -coordinate for M when $x=2$

See Solution

1 ...100 101 102 103

Function

Problem 10201

Determine if the car is moving left or right at $t=8$ for the function $s(t)=-4 t^{3}-10 t^{2}+t-4$ .

Problem 10202

Find the acceleration function $a(t)$ for the particle with position $s(t)=-3t^{2}-t+1$ (in meters) at time $t$ .

Problem 10203

Find the acceleration of the particle at $t=3$ seconds for the function $s(t)=t^{3}-3 t^{2}-8 t+1$ . Answer in $\mathrm{ft} / \mathrm{s}^{2}$ .

Problem 10204

Determine if the train, described by $s(t)=t^{4}-2 t^{3}-5 t^{2}+3$ , is speeding up or slowing down at $t=2$ seconds.

Problem 10205

Find the interval(s) where the hummingbird slows down for $s(t)=-t^{3}+9 t^{2}-24 t-4$ , $t \geq 0$ .

Problem 10206

Graph the function $f(x)=|x+4|-4$ and identify its domain and range.

Problem 10207

A potato is shot up with a speed of $34 \mathrm{ft/s}$ from a 15 ft tall building. Find how long it's in the air using $s(t)=-16 t^{2}+34 t+15$ .

Problem 10208

Problem 10209

The mgf of a random variable $X$ is given by $m(t)=\left(0,9+0.1 e^{t}\right)^{3}$ , then $p(X=1)$ is equal to a. 0.0243 b. 0.536 c. 0.027 d. 0.725 e. 0.9

Problem 10210

Marked out of 1.00
The moment generating function of a random variable X is given by $m(t)=0.3 e^{-t}+0.4+0.3 e^{2 t}$ . Then the mean of X is given by a. 0.4 b. 0.3 c. 0.9 d. 1 e. 2.4

Problem 10211

Find the interval(s) where the car moves left for $s(t)=-t^{3}+6 t^{2}+36 t+4$ with $t \geq 0$ .

Problem 10212

Find the ball's velocity when it first reaches $880 \mathrm{ft}$ , given $s(t)=-16 t^{2}+256 t$ .

Problem 10213

$f(x)=x e^{x}-x$ is concave up ou?

Problem 10214

Problem 10215

- A është vlerësues i pazhvendosur? Pse? 5.24. Shqyrtojmë shpërndarjen eksponenciale të zhvendosur me densitet $f(x)=\lambda e^{-\lambda(x-s)}$ $k u X \geq 5$ . Gjeni me anë të metodës së përgjasisë maksimale një vlerësues për $\lambda$ ?

Problem 10216

B) If the function $f(x)=a x^{3}-3 x^{2}+b x+c$ has a local minimum at -5 and a local maximum at $x=\frac{-1}{2}$ and inflection point at $x=\frac{1}{4}$ find $a, b, c \in R$ .

Problem 10217

Q3: A) Let M be a point moving on the curve $y^{2}=x^{3}$ such that rate of change the point $M$ getting away from of the origin point is 4 unit $/ \mathrm{s}$ . Find the rate of chang of the x -coordinate for M when $x=2$

Start learning now

Download Studdy AI Tutor now. Learn with ease and get all help you need to be successful at school.

Function

Problem 10201

Determine if the car is moving left or right at t=8t=8t=8 for the function s(t)=−4t3−10t2+t−4s(t)=-4 t^{3}-10 t^{2}+t-4s(t)=−4t3−10t2+t−4.

Problem 10202

Find the acceleration function a(t)a(t)a(t) for the particle with position s(t)=−3t2−t+1s(t)=-3t^{2}-t+1s(t)=−3t2−t+1 (in meters) at time ttt.

Problem 10203

Find the acceleration of the particle at t=3t=3t=3 seconds for the function s(t)=t3−3t2−8t+1s(t)=t^{3}-3 t^{2}-8 t+1s(t)=t3−3t2−8t+1. Answer in ft/s2\mathrm{ft} / \mathrm{s}^{2}ft/s2.

Problem 10204

Determine if the train, described by s(t)=t4−2t3−5t2+3s(t)=t^{4}-2 t^{3}-5 t^{2}+3s(t)=t4−2t3−5t2+3, is speeding up or slowing down at t=2t=2t=2 seconds.

Problem 10205

Find the interval(s) where the hummingbird slows down for s(t)=−t3+9t2−24t−4s(t)=-t^{3}+9 t^{2}-24 t-4s(t)=−t3+9t2−24t−4, t≥0t \geq 0t≥0.

Problem 10206

Graph the function f(x)=∣x+4∣−4f(x)=|x+4|-4f(x)=∣x+4∣−4 and identify its domain and range.

Problem 10207

A potato is shot up with a speed of 34ft/s34 \mathrm{ft/s}34ft/s from a 15 ft tall building. Find how long it's in the air using s(t)=−16t2+34t+15s(t)=-16 t^{2}+34 t+15s(t)=−16t2+34t+15.

Problem 10208

Problem 10209

The mgf of a random variable XXX is given by m(t)=(0,9+0.1et)3m(t)=\left(0,9+0.1 e^{t}\right)^{3}m(t)=(0,9+0.1et)3, then p(X=1)p(X=1)p(X=1) is equal to a. 0.0243 b. 0.536 c. 0.027 d. 0.725 e. 0.9

Problem 10210

Marked out of 1.00The moment generating function of a random variable X is given by m(t)=0.3e−t+0.4+0.3e2tm(t)=0.3 e^{-t}+0.4+0.3 e^{2 t}m(t)=0.3e−t+0.4+0.3e2t. Then the mean of X is given by a. 0.4 b. 0.3 c. 0.9 d. 1 e. 2.4

Problem 10211

Find the interval(s) where the car moves left for s(t)=−t3+6t2+36t+4s(t)=-t^{3}+6 t^{2}+36 t+4s(t)=−t3+6t2+36t+4 with t≥0t \geq 0t≥0.

Problem 10212

Find the ball's velocity when it first reaches 880ft880 \mathrm{ft}880ft, given s(t)=−16t2+256ts(t)=-16 t^{2}+256 ts(t)=−16t2+256t.

Problem 10213

f(x)=xex−xf(x)=x e^{x}-xf(x)=xex−x is concave up ou?

Problem 10214

Problem 10215

Problem 10216

B) If the function f(x)=ax3−3x2+bx+cf(x)=a x^{3}-3 x^{2}+b x+cf(x)=ax3−3x2+bx+c has a local minimum at -5 and a local maximum at x=−12x=\frac{-1}{2}x=2−1​ and inflection point at x=14x=\frac{1}{4}x=41​ find a,b,c∈Ra, b, c \in Ra,b,c∈R.

Problem 10217

Q3: A) Let M be a point moving on the curve y2=x3y^{2}=x^{3}y2=x3 such that rate of change the point MMM getting away from of the origin point is 4 unit /s/ \mathrm{s}/s. Find the rate of chang of the x -coordinate for M when x=2x=2x=2

Start learning now

Download Studdy AI Tutor now. Learn with ease and get all help you need to be successful at school.

Determine if the car is moving left or right at $t=8$ for the function $s(t)=-4 t^{3}-10 t^{2}+t-4$ .

Find the acceleration function $a(t)$ for the particle with position $s(t)=-3t^{2}-t+1$ (in meters) at time $t$ .

Find the acceleration of the particle at $t=3$ seconds for the function $s(t)=t^{3}-3 t^{2}-8 t+1$ . Answer in $\mathrm{ft} / \mathrm{s}^{2}$ .

Determine if the train, described by $s(t)=t^{4}-2 t^{3}-5 t^{2}+3$ , is speeding up or slowing down at $t=2$ seconds.

Find the interval(s) where the hummingbird slows down for $s(t)=-t^{3}+9 t^{2}-24 t-4$ , $t \geq 0$ .

Graph the function $f(x)=|x+4|-4$ and identify its domain and range.

A potato is shot up with a speed of $34 \mathrm{ft/s}$ from a 15 ft tall building. Find how long it's in the air using $s(t)=-16 t^{2}+34 t+15$ .

The mgf of a random variable $X$ is given by $m(t)=\left(0,9+0.1 e^{t}\right)^{3}$ , then $p(X=1)$ is equal to a. 0.0243 b. 0.536 c. 0.027 d. 0.725 e. 0.9

Marked out of 1.00
The moment generating function of a random variable X is given by $m(t)=0.3 e^{-t}+0.4+0.3 e^{2 t}$ . Then the mean of X is given by a. 0.4 b. 0.3 c. 0.9 d. 1 e. 2.4

Find the interval(s) where the car moves left for $s(t)=-t^{3}+6 t^{2}+36 t+4$ with $t \geq 0$ .

Find the ball's velocity when it first reaches $880 \mathrm{ft}$ , given $s(t)=-16 t^{2}+256 t$ .

$f(x)=x e^{x}-x$ is concave up ou?

B) If the function $f(x)=a x^{3}-3 x^{2}+b x+c$ has a local minimum at -5 and a local maximum at $x=\frac{-1}{2}$ and inflection point at $x=\frac{1}{4}$ find $a, b, c \in R$ .

Q3: A) Let M be a point moving on the curve $y^{2}=x^{3}$ such that rate of change the point $M$ getting away from of the origin point is 4 unit $/ \mathrm{s}$ . Find the rate of chang of the x -coordinate for M when $x=2$