User George S

2 votes

2 answers

638 views

Suppose A, B and C are sets such that #A=#B. Is it true that #(A x C) =#(B x C)? If it is, prove that. [duplicate]

asked Dec 7, 2016 at 3:29

2 votes

1 answer

12k views

Find the tangent plane to the surface with parametric equations $x=u^2, y=v^2, z=u+2v$ at the point $s(1, 1, 3)$.

asked Nov 20, 2017 at 15:52

2 votes

1 answer

64 views

Solve the initial value problem $y′=(x+y−2)^2$?

asked Jan 31, 2018 at 1:46

2 votes

3 answers

456 views

Understanding of Material Implication

asked Feb 9, 2018 at 7:16

2 votes

1 answer

2k views

Calculating the sample mean and sample standard deviation from confidence interval

asked Feb 26, 2018 at 5:23

1 vote

2 answers

87 views

Find a general solution and check if it is independent for $y''=0$?

asked Mar 11, 2018 at 3:22

1 vote

0 answers

2k views

Let pX(x) = x/15, x = 1, 2, 3, 4, 5, zero elsewhere, be the pmf of X. Find P(X = 1 or 2), P( 1/2 < X < 5/2 ), and P(1 ≤ X ≤ 2).

asked Oct 18, 2018 at 4:29

1 vote

2 answers

777 views

Consider the function f : R-->R defined by f(x) =x^7+x+1. Show that f has an inverse

asked Dec 5, 2016 at 2:57

1 vote

2 answers

719 views

Compute $E[X^2]$ for a random variable $X∼Unif(0,3)$?

asked Jun 7, 2017 at 17:24

1 vote

1 answer

59 views

Suppose $A$ and $B$ are sets with $\#A=\#\mathbb{Z}$ and $\#B=\#\mathbb{Z}$. (a) Prove $\#(A\cup B)=\#\mathbb{Z}$. (b) Is $\#(A\cap B)=\#\mathbb{Z}$?

asked Dec 20, 2016 at 22:41

1 vote

1 answer

31 views

For what $A,B \subset \mathbb R$ is $\{(x,y) \in A \times B \mid x^2-y^2=0\}$ a well defined bijection?

asked Dec 21, 2016 at 23:08

1 vote

1 answer

18 views

A set $A$ is given and a relation $R$ is defined on $A$. Determine whether each is an equivalence relation. Be sure to prove your answer.

asked Oct 27, 2016 at 1:55

1 vote

2 answers

52 views

Find all solutions $ x $in $Z$ to the simultaneous congruences for $x=1 (mod 2)$ and $x=2 (mod 3)$

asked Nov 17, 2016 at 1:19

1 vote

2 answers

3k views

Which of the following sets are closed under addition?

asked Nov 25, 2016 at 19:36

0 votes

0 answers

1k views

Proving a prime $p$ divides $n$ if and only if $p^2$ divides $n^2$

asked Sep 29, 2016 at 0:50

0 votes

1 answer

50 views

Suppose a in an integer, and p is prime. Prove that if $gcd(a,p)>1$, then $p$ divides $a$

asked Oct 5, 2016 at 5:01

0 votes

1 answer

51 views

Describe $R \circ Q$ and $Q \circ R$ in the case where $A=\{1,2\}, R=\{(1,1),(1,2)\}$ and $Q=\{(2,1)\}$

asked Oct 27, 2016 at 4:20

0 votes

0 answers

51 views

How to prove $\frac{1}{1}+\frac{1}{2}+\frac{1}{3}+\frac{1}{4}+...+\frac{1}{2^n}≥1+\frac{n}{2}$

asked Nov 10, 2016 at 0:26

0 votes

1 answer

1k views

Is a log-normal random variable plus a positive constant still log-normal? [closed]

asked May 29, 2017 at 15:53

0 votes

1 answer

761 views

Let $X_1, \cdots ,X_n$ be independent and identically distributed random variables. [duplicate]

asked Jun 1, 2017 at 21:39

0 votes

3 answers

1k views

How to verify the formula for the moment generating function of a uniform random variable?

asked Jun 4, 2017 at 22:12

0 votes

1 answer

35 views

How to write down the density, the expected value and the variance of a random variable distributed as an exp(γ)? [closed]

asked Jun 5, 2017 at 18:43

0 votes

1 answer

2k views

Find the volume of the tetrahedron bounded by the planes x+2y-z=2, x=2y, x=0, and z=0.

asked Oct 3, 2017 at 5:09

0 votes

1 answer

150 views

Prove that linear maps on $x\in\mathbb{R}^n$ are differentiable

asked Jan 24, 2018 at 2:33

0 votes

3 answers

104 views

Use the definition of the limit to verify $\lim\limits_{(x,y,z) \to 0} \frac {(5x^3y^2+6xz^4)}{(2x^2+3y^2+z^2)}$ [closed]

asked Jan 24, 2018 at 4:29

0 votes

1 answer

60 views

Suppose that $X_1$ and $X_2$ are continuous random variables with joint cdf $F(x_1,x_2)$ and marginal cdfs $F_1 (x_1)$ and $F_2 (x_2)$ respectively.

asked Oct 31, 2018 at 23:40

0 votes

1 answer

141 views

In the finite field $\mathbb{F}_{101}$ ,where discrete logarithms are $L_2(3)=69$ and $L_2(5)=24$. Compute the discrete logarithm $ L_2(60)$?

asked Nov 18, 2018 at 19:08

0 votes

1 answer

31 views

Find the power series representation?

asked Mar 27, 2018 at 0:04

0 votes

2 answers

1k views

Find the least squares error vector e=b-Ax resulting from the least squares solution x and verify that it is orthogonal to the column space of A?

asked Mar 29, 2018 at 19:33

-1 votes

1 answer

63 views

Find all x in Z8 satisfying [2]x+[4]=[2]

asked Nov 15, 2016 at 2:47

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31 Questions

Suppose A, B and C are sets such that #A=#B. Is it true that #(A x C) =#(B x C)? If it is, prove that. [duplicate]

Find the tangent plane to the surface with parametric equations $x=u^2, y=v^2, z=u+2v$ at the point $s(1, 1, 3)$.

Solve the initial value problem $y′=(x+y−2)^2$?

Understanding of Material Implication

Calculating the sample mean and sample standard deviation from confidence interval

Find a general solution and check if it is independent for $y''=0$?

Let pX(x) = x/15, x = 1, 2, 3, 4, 5, zero elsewhere, be the pmf of X. Find P(X = 1 or 2), P( 1/2 < X < 5/2 ), and P(1 ≤ X ≤ 2).

Consider the function f : R-->R defined by f(x) =x^7+x+1. Show that f has an inverse

Compute $E[X^2]$ for a random variable $X∼Unif(0,3)$?

Suppose $A$ and $B$ are sets with $\#A=\#\mathbb{Z}$ and $\#B=\#\mathbb{Z}$. (a) Prove $\#(A\cup B)=\#\mathbb{Z}$. (b) Is $\#(A\cap B)=\#\mathbb{Z}$?

For what $A,B \subset \mathbb R$ is $\{(x,y) \in A \times B \mid x^2-y^2=0\}$ a well defined bijection?

A set $A$ is given and a relation $R$ is defined on $A$. Determine whether each is an equivalence relation. Be sure to prove your answer.

Find all solutions $ x $in $Z$ to the simultaneous congruences for $x=1 (mod 2)$ and $x=2 (mod 3)$

Which of the following sets are closed under addition?

Proving a prime $p$ divides $n$ if and only if $p^2$ divides $n^2$

Suppose a in an integer, and p is prime. Prove that if $gcd(a,p)>1$, then $p$ divides $a$

Describe $R \circ Q$ and $Q \circ R$ in the case where $A=\{1,2\}, R=\{(1,1),(1,2)\}$ and $Q=\{(2,1)\}$

How to prove $\frac{1}{1}+\frac{1}{2}+\frac{1}{3}+\frac{1}{4}+...+\frac{1}{2^n}≥1+\frac{n}{2}$

Is a log-normal random variable plus a positive constant still log-normal? [closed]

Let $X_1, \cdots ,X_n$ be independent and identically distributed random variables. [duplicate]

How to verify the formula for the moment generating function of a uniform random variable?

How to write down the density, the expected value and the variance of a random variable distributed as an exp(γ)? [closed]

Find the volume of the tetrahedron bounded by the planes x+2y-z=2, x=2y, x=0, and z=0.

Prove that linear maps on $x\in\mathbb{R}^n$ are differentiable

Use the definition of the limit to verify $\lim\limits_{(x,y,z) \to 0} \frac {(5x^3y^2+6xz^4)}{(2x^2+3y^2+z^2)}$ [closed]

Suppose that $X_1$ and $X_2$ are continuous random variables with joint cdf $F(x_1,x_2)$ and marginal cdfs $F_1 (x_1)$ and $F_2 (x_2)$ respectively.

In the finite field $\mathbb{F}_{101}$ ,where discrete logarithms are $L_2(3)=69$ and $L_2(5)=24$. Compute the discrete logarithm $ L_2(60)$?

Find the power series representation?

Find the least squares error vector e=b-Ax resulting from the least squares solution x and verify that it is orthogonal to the column space of A?

Find all x in Z8 satisfying [2]x+[4]=[2]