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Recent questions tagged prove


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Prove that \(A \cup A=A\)
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Prove that \(A \cup A=A\)Prove that \(A \cup A=A\) ...
by MathsGee Platinum
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asked in Mathematics Jan 8
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Prove Gibb's lemma
1 answer 17 views
Prove Gibb's lemma(Gibb's Lemma). Assume \(\left(p_{1}, \ldots, p_{m}\right)\) is probability distribution and let \(\left(r_{1}, \ldots, r_{m}\right)\) be such that \( ...
by MathsGee Platinum
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asked in Mathematics Jan 8
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Prove the following theorem:
1 answer 16 views
Prove the following theorem:Prove the following theorem: Let \(n\) and \(m\) be integers. Then i. if \(n\) and \(m\) are both even, then \(n+m\) is even, ii. if \(n\) and \(m\) ...
by MathsGee Platinum
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asked in Mathematics Jan 8
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What is a random variable in statistics?
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What is a random variable in statistics?What is a random variable in statistics? ...
by Pieter SIlver Status
(17,435 points)
asked in Data Science & Statistics Dec 16, 2021
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Prove Bayes Rule
1 answer 31 views
Prove Bayes RuleProve Bayes Rule (Bayes Rule). Let \(A\) and \(B\) be two subsets of our sample space \(\Omega\). Then \ P(A \mid B)=\frac{P(B \mid A) P(A)}{P(B)} \ ...
by Pieter SIlver Status
(17,435 points)
asked in Data Science & Statistics Dec 16, 2021
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Prove Chebyschev’s inequality
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Prove Chebyschev’s inequalityProve Chebyschev’s inequality (Chebyschev's inequality). Let \(X\) be a random variable. Then \ P(|X-E X|>\epsilon) \leq \frac{\operato ...
by MathsGee Platinum
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asked in Data Science & Statistics Dec 15, 2021
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Prove Markov’s inequality.
1 answer 41 views
Prove Markov’s inequality.Prove (Markov's inequality). Suppose \(X\) is a nonnegative random variable and \(a \in\) is a positive constant. Then \ P(X \geq a) \leq \frac{E X} ...
by MathsGee Platinum
(102,810 points)
asked in Data Science & Statistics Dec 15, 2021
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If \(X\) and \(Y\) are independent random variables, then \[ \operatorname{Var}(X+Y)=\operatorname{Var}(X)+\operatorname{Var}(Y) \]
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Prove that if \(X\) is a random variable with mean \(E X\) and \(c \in\) is \(a\) real number, then \(\operatorname{Var}(X)=E\left(X^{2}\right)-E(X)\)

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Prove that if \(X\) is a random variable with mean \(E X\) and \(c \in\) is \(a\) real number, then \(\operatorname{Var}(c X)=c^{2} \operatorname{Var}(X)\)

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Prove that if \(X\) is a random variable with mean \(E X\) and \(c \in\) is \(a\) real number, then \(\operatorname{Var}(X) \geq 0\).
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Prove that, for all values of \(x\), \[ x^{2}+4 x+12>x+3 \]
1 answer 27 views
Prove that, for all values of \(x\), \[ x^{2}+4 x+12>x+3 \]Prove that, for all values of \(x\), \ x^{2}+4 x+12>x+3 \ ...
by MathsGee Platinum
(102,810 points)
asked in Mathematics Nov 9, 2021
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Prove the following
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Prove the followingProve that $ cos(x+y) \cdot cos(x-y) = cos^2x-sin^2y$ ...
by Claudia Wooden
(4,756 points)
asked in Mathematics Oct 7, 2021
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Prove the following trig identity
1 answer 23 views
Prove the following trig identityProve the identity: $\frac{1}{cos \theta}- \frac{cos \theta}{1+ sin \theta} = tan \theta$ ...
by Claudia Wooden
(4,756 points)
asked in Mathematics Oct 7, 2021
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Maximum value
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Maximum valueShow that the maximum value of $\sqrt{-x^2+4x+12}$ is $4$ ...
by Claudia Wooden
(4,756 points)
asked in Mathematics Oct 7, 2021
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Determine if \(a_{n}=1-1.1+1.11-1.111+1.1111-\ldots\) converges and find the sums when they exist?
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Prove the martingale convergence theorem
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Prove the martingale convergence theoremProve the martingale convergence theorem ...
by MathsGee Platinum
(102,810 points)
asked in Data Science & Statistics Sep 21, 2021
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Prove the Prohorov inequality
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Prove Kolmogorov's inequality
1 answer 30 views
Prove Kolmogorov's inequalityProve Kolmogorov's inequality ...
by MathsGee Platinum
(102,810 points)
asked in Data Science & Statistics Sep 21, 2021
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Prove the Chernoff-Cramer bound
1 answer 15 views
Prove the Chernoff-Cramer boundProve the Chernoff-Cramer bound ...
by MathsGee Platinum
(102,810 points)
asked in Data Science & Statistics Sep 21, 2021
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Prove the Bernstein inequalities
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Prove the Bernstein inequalitiesProve the Bernstein inequalities ...
by MathsGee Platinum
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asked in Data Science & Statistics Sep 21, 2021
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Prove the Bennett inequality
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Prove the Bennett inequalityProve the Bennett inequality ...
by MathsGee Platinum
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asked in Data Science & Statistics Sep 21, 2021
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What is the radian measure of a circle?
1 answer 57 views
What is the radian measure of a circle?What is the radian measure of a circle? ...
by MathsGee Platinum
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asked in Mathematics Sep 19, 2021
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Given that \(\sin x=\frac{5}{13}\) and \(\sin y=\frac{8}{17}\), where \(x\) and \(y\) are acute, find \(\cos (x+y)\)
1 answer 51 views
Given that \(\sin x=\frac{5}{13}\) and \(\sin y=\frac{8}{17}\), where \(x\) and \(y\) are acute, find \(\cos (x+y)\)Given that \(\sin x=\frac{5}{13}\) and \(\sin y=\frac{8}{17}\), where \(x\) and \(y\) are acute, find \(\cos (x+y)\) A. \(\frac{130}{221}\) B. \(\fra ...
by Siyavula Bronze Status
(7,016 points)
asked in Mathematics Sep 11, 2021
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Complete the square for \(3 x^{2}+5 x+4\)
1 answer 30 views
Complete the square for \(3 x^{2}+5 x+4\)Complete the square for \(3 x^{2}+5 x+4\) ...
by Siyavula Bronze Status
(7,016 points)
asked in Mathematics Sep 11, 2021
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