Recent questions tagged estimate

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Given: $4-2 x<16$ where $x \in \mathbb{Z}$

asked Jun 22 in Mathematics by ♦MathsGee Platinum (122,714 points) | 15 views

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Use Newton's Method to determine $x_{2}$ for the given function and given value of $x_{0}$.

asked Feb 1 in Mathematics by ♦MathsGee Platinum (122,714 points) | 127 views

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Suppose that \[ f(x)= \begin{cases}e^{-1 / x^{2}} & \text { if } x \neq 0 \\ 0 & \text { if } x=0\end{cases} \]

asked Feb 1 in Mathematics by ♦MathsGee Platinum (122,714 points) | 92 views

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Prove that $\ln x \leq x-1$ for $x>0$

asked Jan 8 in Mathematics by ♦MathsGee Platinum (122,714 points) | 100 views

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How do you estimate the bias of a coin?

asked Dec 15, 2021 in Data Science & Statistics by ♦MathsGee Platinum (122,714 points) | 100 views

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'Given that the future is unknown, the best we can do is to estimate the likelihood of future events and then use expected profit as the decision criterion.' Discuss.

asked Nov 16, 2021 in Economics and Finance by ♦MathsGee Platinum (122,714 points) | 262 views

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Let $X$ be a continuous random variable with p.d.f: \[ f(x)= \begin{cases}a x, & 0<x \leq 1 \\ a, & 1 \leq x \leq 2 \\ -a x+3 a, & 2 \leq x \leq 3 \\ 0, & \text { otherwise }\end{cases} \]

asked Oct 16, 2021 in Data Science & Statistics by ♦MathsGee Platinum (122,714 points) | 222 views

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Which of these is the smallest approximate sample size required to obtain the desired margin of error?

asked Sep 14, 2021 in Data Science & Statistics by ♦MathsGee Platinum (122,714 points) | 168 views

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Use Newton's Method to determine $x_{2}$ for the given function and given value of $x_{0}$.$f(x)=x^{3}-7 x^{2}+8 x-3, x_{0}=5$

asked Aug 17, 2021 in Mathematics by Siyavula Bronze Status (7,578 points) | 132 views

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If $\mathrm{A}=\left[(\mathrm{x}, \mathrm{y}): \mathrm{x}^{2}+\mathrm{y}^{2}=25\right]$ and $\mathrm{B}=\left[(\mathrm{x}, \mathrm{y}): \mathrm{x}^{2}+9 \mathrm{y}^{2}=144\right]$, then $\mathrm{A} \cap \mathrm{B}$ contains $\mathrm{points}$.

asked Aug 7, 2021 in Mathematics by ♦MathsGee Platinum (122,714 points) | 102 views

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What property of real numbers would simplify the following expression: $4+7(x-1) ?$

asked Jul 29, 2021 in Mathematics by ♦MathsGee Platinum (122,714 points) | 130 views

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Simplify the following algebraic expression: $\frac{16 x^{2}}{4 x}-\frac{21 x^{3} y^{2}}{7 x^{2} y^{2}}$

asked Jun 17, 2021 in Mathematics by Maths Genie Bronze Status (5,586 points) | 88 views

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A human resource manager is trying to estimate the cost of a workforce accident.

asked Jun 17, 2021 in Mathematics by Maths Genie Bronze Status (5,586 points) | 104 views

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Simplify $9 x+3 y-\frac{7}{2} x+4 y$

asked Jun 17, 2021 in Mathematics by Maths Genie Bronze Status (5,586 points) | 107 views

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Simplify the following surds

asked Jun 14, 2021 in Mathematics by Student SIlver Status (10,980 points) | 126 views

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What new ideas about mathematics have you learnt recently?

asked Jun 14, 2021 in Mathematics by ♦MathsGee Platinum (122,714 points) | 79 views

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Carry out a test of significance for $H_{0}: \mu=40 \mathrm{hrs}$ vs $H_{1} \mu>40 \mathrm{hrs} . \alpha=0.05$

asked Jun 14, 2021 in Data Science & Statistics by ♦MathsGee Platinum (122,714 points) | 78 views

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Find the density that will maximize the hourly flow.

asked Jun 11, 2021 in Mathematics by ♦MathsGee Platinum (122,714 points) | 99 views

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If $|z+4| \leq 3$ then the maximum value of $|z+1|$ is

asked Jun 9, 2021 in Mathematics by ♦MathsGee Platinum (122,714 points) | 143 views

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If $z=x-i y$ and $z^{\frac{1}{3}}=p+i q$, then $\frac{\left(\frac{x}{p}+\frac{y}{q}\right)}{\left(p^{2}+q^{2}\right)}$ is equal to

asked Jun 9, 2021 in Mathematics by ♦MathsGee Platinum (122,714 points) | 167 views

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If $\left(\frac{1+i}{1-i}\right)^{x}=1$, then

asked Jun 9, 2021 in Mathematics by ♦MathsGee Platinum (122,714 points) | 84 views

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Let $f(x)=(x+1)^{2}-1, x \geq-1$

asked Jun 9, 2021 in Mathematics by ♦MathsGee Platinum (122,714 points) | 99 views

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What is the minimum value that the expression $$ \frac{x^{2} y^{2}-2 x^{2} y+2 x^{2}+2 x y-2 x+1}{x^{2} y+x} $$ where $x, y \in \mathbb{R}^{+}$, can attain?

asked May 31, 2021 in Mathematics by ♦Pieter Diamond (40,709 points) | 127 views

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For $x, y, z \in \mathbb{R}^{+}$ prove that $x^{2}+y^{2}+z^{2} \geq x \sqrt{y^{2}+z^{2}}+y \sqrt{x^{2}+z^{2}}$.

asked May 31, 2021 in Mathematics by ♦MathsGee Platinum (122,714 points) | 184 views

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Harley surveyed his classmates about how many siblings they have and got the following data: $0,1,3,5,4,2,2,9,1,2,0,1,1,1,1,3$ Which measure is best measure of center of the data?

asked May 31, 2021 in Data Science & Statistics by ♦MathsGee Platinum (122,714 points) | 231 views

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Suppose $X$ is $\mathrm{N}\left(\mu, \sigma^{2}\right)$. For $a=1,2,3$ find $P(|X-\mu|<a \sigma)$.

asked May 30, 2021 in Data Science & Statistics by ♦MathsGee Platinum (122,714 points) | 184 views

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Suppose $X$ is $\mathrm{N}(-1,4)$. Find

asked May 30, 2021 in Data Science & Statistics by ♦MathsGee Platinum (122,714 points) | 119 views

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Suppose $X$ is $\mathrm{N}(10,1) .$ Find (i) $P[X>10.5]$, (ii) $P[9.5<X<11]$, (iii) $x$ such that $P[X<x]=0.95$.

asked May 30, 2021 in Data Science & Statistics by ♦MathsGee Platinum (122,714 points) | 236 views

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Let the random variable $X$ have the density $f(x)=k x$ if $0 \leq x \leq 3$. Find $k$. Find $x_{1}$ and $x_{2}$ such that $P\left(X \leq x_{1}\right)=0.1$ and $P\left(X \leq x_{2}\right)=0.95 .$ Find $P(|X-1.8|<0.6)$.

asked May 30, 2021 in Data Science & Statistics by ♦MathsGee Platinum (122,714 points) | 214 views

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Let $X$ have the density $f(x)=2 x$ if $0 \leq x \leq 1$ and $f(x)=0$ otherwise. Show that $X$ has the mean $2 / 3$ and the variance $1 / 18$. Find the mean and the variance of the random variable $Y=-2 X+3$.

asked May 30, 2021 in Data Science & Statistics by ♦MathsGee Platinum (122,714 points) | 209 views

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What is the area of the portion of the surface $z=x^{2}+y^{2}$ lying inside the cylinder $x^{2}+y^{2}=4$ in $x y z$ -space?

asked May 30, 2021 in Mathematics by ♦MathsGee Platinum (122,714 points) | 128 views

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How do you form numerals from digits?

asked May 24, 2021 in Mathematics by ♦Pieter Diamond (40,709 points) | 103 views

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In a presidential election, there are four candidates. Call them $\mathrm{A}, \mathrm{B}, \mathrm{C}$, and $\mathrm{D}$.

asked May 22, 2021 in Data Science & Statistics by ♦Pieter Diamond (40,709 points) | 385 views

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Let $f(z)$ be the principal branch of $\sqrt[3]{z}$.

asked May 10, 2021 in Mathematics by ♦Pieter Diamond (40,709 points) | 209 views

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Show that $$ |\cos (z)|^{2}=(\cos x)^{2}+(\sinh y)^{2} $$ for all $z \in \mathbb{C}$, where $x=\operatorname{Re}(z)$ and $y=\operatorname{Im}(z)$

asked May 10, 2021 in Mathematics by ♦Pieter Diamond (40,709 points) | 393 views

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Show that $$ |\sin z|^{2}=(\sin x)^{2}+(\sinh y)^{2} $$ for all complex numbers $z=x+y i$.

asked May 10, 2021 in Mathematics by ♦Pieter Diamond (40,709 points) | 726 views

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Show that $$ |\log (z)| \leq|\ln | z||+\pi $$ for all $z \neq 0$

asked May 10, 2021 in Mathematics by ♦Pieter Diamond (40,709 points) | 145 views

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Show that $$ \frac{R^{4}-R}{R^{2}+R+1} \leq\left|\frac{z^{4}+i z}{z^{2}+z+1}\right| \leq \frac{R^{4}+R}{(R-1)^{2}} $$ for all $z$ satisfying $|z|=R>1$.

asked May 10, 2021 in Mathematics by ♦Pieter Diamond (40,709 points) | 155 views

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Determine the best value of $h$ for the greatest accuracy of the answer. How many digits accuracy can you expect with this choice of $h ?$

asked May 9, 2021 in Mathematics by ♦MathsGee Platinum (122,714 points) | 166 views

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Show that for any $n$, there is a $z \in[a, b]$ such that $z$ has period $n$ under $f$.

asked May 9, 2021 in Mathematics by ♦MathsGee Platinum (122,714 points) | 90 views

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Assume that $f_{\mu}(x)=\mu \cdot x \cdot(1-x)$. Show that if $1 \leq \mu \leq 3$, then $f_{\mu}^{n}(x) \rightarrow 1-\frac{1}{\mu}$ as $n \rightarrow \infty$ for all $0<x<1$.

asked May 9, 2021 in Mathematics by ♦MathsGee Platinum (122,714 points) | 107 views

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Show that if $0 \leq \mu \leq 1$, then $f_{\mu}^{n}(x) \rightarrow 0$ as $n \rightarrow \infty$ for all $0 \leq x \leq 1$.

asked May 9, 2021 in Mathematics by ♦MathsGee Platinum (122,714 points) | 122 views

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Show that the Newton-Raphson method converges quadratically. That is, suppose that the fixed point is $z$ and that the error of the $n$ th iteration is $\left|x_{n}-z\right|=h$, then $\left|x_{n+1}-z\right| \approx h^{2}$ for $h$ small enough.

asked May 9, 2021 in Mathematics by ♦MathsGee Platinum (122,714 points) | 200 views

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Show that there is an $\varepsilon>0$ such that for any $x_{0} \in$ $[z-\varepsilon, z+\varepsilon], g^{n}\left(x_{0}\right) \rightarrow z$ as $n \rightarrow \infty$

asked May 9, 2021 in Mathematics by ♦MathsGee Platinum (122,714 points) | 191 views

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Let $h$ be a continuous function $h: R^{n} \rightarrow R^{n}$. Let $x_{0} \in R^{n} .$ Suppose that $h^{n}\left(x_{0}\right) \rightarrow z$ as $n \rightarrow \infty$. Show that $h(z)=z$

asked May 9, 2021 in Mathematics by ♦MathsGee Platinum (122,714 points) | 176 views

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Estimate the error of $Q(90)$ and find an extrapolated approximation.

asked May 9, 2021 in Mathematics by ♦MathsGee Platinum (122,714 points) | 79 views

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Derive a formula to extrapolate the $Q(n)$ to get, $\tilde{Q}(n)$, a better estimate of $I$.

asked May 9, 2021 in Mathematics by ♦MathsGee Platinum (122,714 points) | 86 views

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Suppose that one estimates a quantity $I$ by its numerical approximation, $Q(n)$ for $n=10,30,90, \ldots$ It is known that $|I-Q(n)|=\mathrm{O}\left(n^{-4}\right)$ as $n \rightarrow \infty$.

asked May 9, 2021 in Mathematics by ♦MathsGee Platinum (122,714 points) | 112 views

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Why is it difficult to estimate individual treatment effects in Causal Inference?

asked May 8, 2021 in Data Science & Statistics by ♦Pieter Diamond (40,709 points) | 97 views

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An Olympic athlete of mass $80kg$ competes in a race. What is the best estimate of his kinetic energy during the race?

asked Apr 13, 2021 in Physics & Chemistry by ♦MathsGee Platinum (122,714 points) | 280 views

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