Function

Problem 10201

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

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Problem 10202

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

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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 $\mathrm{ft} / \mathrm{s}^{2}$ .

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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.

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Problem 10205

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

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Problem 10206

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

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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 $s(t)=-16 t^{2}+34 t+15$ .

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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.

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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

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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

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Problem 10211

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

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Problem 10212

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

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Problem 10213

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

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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) $x=2 \ln 5$

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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 $\lambda$ ?

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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 $a, b, c \in R$ .

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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 $x=2$

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Problem 10218

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

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Problem 10219

Kathryn fills a $100 \mathrm{ft}^{3}$ container with sand at $1.25 \mathrm{ft}^{3} / \mathrm{min}$ . Find $V(t)$ and its domain.

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Problem 10220

Find the car's acceleration at $t=2$ seconds given $s(t)=2 t^{4}-10 t^{3}-5 t^{2}+9$ . Answer in $\mathrm{m} / \mathrm{s}^{2}$ .

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Problem 10221

Find the car's acceleration at $t=2$ seconds, given $s(t)=2 t^{4}-9 t^{3}-6 t^{2}-8$ .

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Problem 10222

Kathryn fills a $100 \mathrm{ft}^{3}$ container with sand at $1.25 \mathrm{ft}^{3}/\mathrm{min}$ . Find $V(t)$ for $t \in [0,4800]$ . Domain: $[0,80]$ , Range: ?

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Problem 10223

Find the interval(s) where the car slows down given $s(t)=-\frac{2 t^{3}}{3}+3 t^{2}+20 t-3$ , $t \geq 0$ .

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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

Problem 10218

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 10219

Kathryn fills a 100ft3100 \mathrm{ft}^{3}100ft3 container with sand at 1.25ft3/min1.25 \mathrm{ft}^{3} / \mathrm{min}1.25ft3/min. Find V(t)V(t)V(t) and its domain.

Problem 10220

Find the car's acceleration at t=2t=2t=2 seconds given s(t)=2t4−10t3−5t2+9s(t)=2 t^{4}-10 t^{3}-5 t^{2}+9s(t)=2t4−10t3−5t2+9. Answer in m/s2\mathrm{m} / \mathrm{s}^{2}m/s2.

Problem 10221

Find the car's acceleration at t=2t=2t=2 seconds, given s(t)=2t4−9t3−6t2−8s(t)=2 t^{4}-9 t^{3}-6 t^{2}-8s(t)=2t4−9t3−6t2−8.

Problem 10222

Kathryn fills a 100ft3100 \mathrm{ft}^{3}100ft3 container with sand at 1.25ft3/min1.25 \mathrm{ft}^{3}/\mathrm{min}1.25ft3/min. Find V(t)V(t)V(t) for t∈[0,4800]t \in [0,4800]t∈[0,4800]. Domain: [0,80][0,80][0,80], Range: ?

Problem 10223

Find the interval(s) where the car slows down given s(t)=−2t33+3t2+20t−3s(t)=-\frac{2 t^{3}}{3}+3 t^{2}+20 t-3s(t)=−32t3​+3t2+20t−3, t≥0t \geq 0t≥0.

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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 $x=2$

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

Kathryn fills a $100 \mathrm{ft}^{3}$ container with sand at $1.25 \mathrm{ft}^{3} / \mathrm{min}$ . Find $V(t)$ and its domain.

Find the car's acceleration at $t=2$ seconds given $s(t)=2 t^{4}-10 t^{3}-5 t^{2}+9$ . Answer in $\mathrm{m} / \mathrm{s}^{2}$ .

Find the car's acceleration at $t=2$ seconds, given $s(t)=2 t^{4}-9 t^{3}-6 t^{2}-8$ .

Kathryn fills a $100 \mathrm{ft}^{3}$ container with sand at $1.25 \mathrm{ft}^{3}/\mathrm{min}$ . Find $V(t)$ for $t \in [0,4800]$ . Domain: $[0,80]$ , Range: ?

Find the interval(s) where the car slows down given $s(t)=-\frac{2 t^{3}}{3}+3 t^{2}+20 t-3$ , $t \geq 0$ .