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Solve a pair of congruences
Draft
Question in Content created by Newcastle University by Newcastle University Mathematics and Statistics

Solving two simultaneous congruences:

$\begin{eqnarray*} c_1x\;&\equiv&\;b_1\;&\mod&\;n_1\\ c_2x\;&\equiv&\;b_2\;&\mod&\;n_2\\ \end{eqnarray*}$ where $\operatorname{gcd}(c_1,n_1)=1,\;\operatorname{gcd}(c_2,n_2)=1,\;\operatorname{gcd}(n_1,n_2)=1$
Solve three congruences with the Chinese Remainder Theorem
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Question in Content created by Newcastle University by Newcastle University Mathematics and Statistics

Solving three simultaneous congruences using the Chinese Remainder Theorem:

$\begin{eqnarray*} x\;&\equiv&\;b_1\;&\mod&\;n_1\\ x\;&\equiv&\;b_2\;&\mod&\;n_2\\x\;&\equiv&\;b_3\;&\mod&\;n_3 \end{eqnarray*}$ where $\operatorname{gcd}(n_1,n_2,n_3)=1$
Construct a probability distribution function, then find CDF and expectation
Draft
Question in Content created by Newcastle University by Newcastle University Mathematics and Statistics

The random variable $X$ has a PDF which involves a parameter $c$ . Find the value of $c$ . Find the distribution function $F_X(x)$ and $P(a \lt X \lt b)$ .

Also find the expectation $\displaystyle \operatorname{E}[X]=\int_{-\infty}^{\infty}xf_X(x)\;dx$ .
PDF and CDF of continuous uniform random variable,
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Question in Content created by Newcastle University by Newcastle University Mathematics and Statistics

$X$ is a continuous uniform random variable defined on $[a,\;b]$ . Find the PDF and CDF of $X$ and find $P(X \ge c)$ .
Julie's copy of Second order differential equations 5
Draft
Question in Julie's workspace by Julie Crowley

Find the general solution of $y''+2py'+(p^2-q^2)y=x$ in the form $Ae^{ax}+Be^{bx}+y_{PI}(x),\;y_{PI}(x)$ a particular integral.

rebelmaths
Second order differential equations - sine forcing
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Question in Daniel's workspace by Daniel Nucinkis

Find the general solution of $y''+2py'+(p^2-q^2)y=A\sin(fx)$ in the form $A_1e^{ax}+B_1e^{bx}+y_{PI}(x),\;y_{PI}(x)$ a particular integral. Use initial conditions to find $A_1,B_1$ .
Ricardo's copy of IS2.2
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Question in Ricardo's workspace by Ricardo Monge

The random variable $X$ has a PDF which involves a parameter $c$ . Find the value of $c$ . Find the distribution function $F_X(x)$ and $P(a \lt X \lt b)$ .
IS2.2
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Question in Bill's workspace by Bill Foster

The random variable $X$ has a PDF which involves a parameter $c$ . Find the value of $c$ . Find the distribution function $F_X(x)$ and $P(a \lt X \lt b)$ .

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