 # Get help with andom variable equations

Recent questions in Random variables sibuzwaW 2021-11-05 Answered

### Random variables X and Y have joint PDF $$f_{X,Y}(x,y)=\begin{cases}12e^{-(3x+4y)},\ x \geq 0, y \geq 0\\0,\ otherwise\end{cases}$$ Find $$\displaystyle{P}{\left[\min{\left({X},{Y}\right)}\geq{2}\right]}$$ Kye 2021-11-05 Answered

### The joint density of the random variables X and Y is given by $$f(x,y)=\begin{cases}8xy & 0\leq x\leq 1, 0\leq y \leq x\\0 & otherwise\end{cases}$$ Find the marginal density of X Brennan Flores 2021-11-04 Answered

### Compute the distribution of X+Y in the following cases: X and Y are independent normal random variables with respective parameters $$\displaystyle{\left(\mu_{{{1}}},{\sigma_{{{1}}}^{{{2}}}}\right)}{\quad\text{and}\quad}{\left(\mu_{{{2}}},{\sigma_{{{2}}}^{{{2}}}}\right)}$$. Dolly Robinson 2021-11-03 Answered

### For continuous random variables X and Y with joint probability density function $$f(x,y)=\begin{cases}xe^{-(x+xy)} & x>0\ and\ y>0\\0 & otherwise\end{cases}$$ Find P(X>1 and Y>1). Trent Carpenter 2021-11-03 Answered

### The joint density of the random variables X and Y is given by $$f(x,y)=\begin{cases}8xy & 0\leq x\leq 1, 0\leq y \leq x\\0 & otherwise\end{cases}$$ Find the conditional density of X Find the conditional density of Y Suman Cole 2021-11-01 Answered

### Two random variables X and Y with joint density function given by: $$f(x,y)=\begin{cases}\frac{1}{3}(2x+4y)& 0\leq x,\leq 1\\0 & elsewhere\end{cases}$$ Find the marginal density of X. sanuluy 2021-11-01 Answered

### Assume that X and Y are jointly continuous random variables with joint probability density function given by $$\displaystyle{f{{\left({x},{y}\right)}}}={b}{e}{g}\in{\left\lbrace{c}{a}{s}{e}{s}\right\rbrace}{\frac{{{1}}}{{{36}}}}{\left({3}{x}-{x}{y}+{4}{y}\right)}\ {\quad\text{if}\quad}\ {0}{<}{x}{<}{2}\ {\quad\text{and}\quad}\ {1}{<}{y}{<}{3}\backslash{0}\ \ \ \ \ {o}{t}{h}{r}{e}{w}{i}{s}{e}{e}{n}{d}{\left\lbrace{c}{a}{s}{e}{s}\right\rbrace}$$ Find the marginal density functions for X and Y . Efan Halliday 2021-10-30 Answered

### Compute the distribution of X+Y in the following cases: X and Y are independent Poisson random variables with means respective $$\displaystyle\lambda_{{{1}}}{\quad\text{and}\quad}\lambda_{{{2}}}$$. generals336 2021-10-28 Answered

### Suppose that the random variables X and Y have joint p.d.f. $$f(x,y)=\begin{cases}kx(x-y),0 Find the marginal p.d.f. of the two random variables. banganX 2021-10-28 Answered ### Suppose that X and Y are continuous random variables with joint pdf \(\displaystyle{f{{\left({x},{y}\right)}}}={e}^{{-{\left({x}+{y}\right)}}}{0}{<}{x}{<}\infty\ {\quad\text{and}\quad}\ {0}{<}{y}{<}\infty$$ and zero otherwise. Find P(X+Y>3) nitraiddQ 2021-10-28 Answered

### Random variable X and Y have the joint PDF $$f_{XY}(x,y)=\begin{cases}c,\ x\geq 0,y\geq 0,(x^{2}+y)\leq 1,\\0,\ \ \ \ \ otherwise \end{cases}$$ Find the marginal PDF $$\displaystyle{{f}_{{{Y}}}{\left({y}\right)}}$$. hexacordoK 2021-10-27 Answered

### Assume that X and Y are jointly continuous random variables with joint probability density function given by $$\displaystyle{f{{\left({x},{y}\right)}}}={b}{e}{g}\in{\left\lbrace{c}{a}{s}{e}{s}\right\rbrace}{\frac{{{1}}}{{{36}}}}{\left({3}{x}-{x}{y}+{4}{y}\right)}\ {\quad\text{if}\quad}\ {0}{<}{x}{<}{2}\ {\quad\text{and}\quad}\ {1}{<}{y}{<}{3}\backslash{0}\ \ \ \ \ {o}{t}{h}{r}{e}{w}{i}{s}{e}{e}{n}{d}{\left\lbrace{c}{a}{s}{e}{s}\right\rbrace}$$ Find Cov(X,Y). abondantQ 2021-10-26 Answered

### Suppose that X and Y are independent rv's with moment generating functions $$\displaystyle{M}_{{{X}}}{\left({t}\right)}$$ and $$\displaystyle{M}_{{{Y}}}{\left({t}\right)}$$, respectively. If Z=X+Y, show that $$\displaystyle{M}_{{{Z}}}{\left({t}\right)}={M}_{{{X}}}{\left({t}\right)}{M}_{{{Y}}}{\left({t}\right)}$$. jernplate8 2021-10-26 Answered

### Consider two continuous random variables X and Y with joint density function $$\displaystyle{f{{\left({x},{y}\right)}}}={b}{e}{g}\in{\left\lbrace{c}{a}{s}{e}{s}\right\rbrace}{x}+{y}\ {o}\leq{x}\leq{1},{0}\leq{y}\leq{1}\backslash{0}\ \ \ \ {o}{t}{h}{e}{r}{w}{i}{s}{e}{e}{n}{d}{\left\lbrace{c}{a}{s}{e}{s}\right\rbrace}$$ P(X>0.8, Y>0.8) is? BenoguigoliB 2021-10-25 Answered

### Suppose that X and Y are continuous random variables with joint pdf $$\displaystyle{f{{\left({x},{y}\right)}}}={e}^{{-{\left({x}+{y}\right)}}}{0}{<}{x}{<}\infty\ {\quad\text{and}\quad}\ {0}{<}{y}{<}\infty$$ and zero otherwise. Find P(X>Y) Tahmid Knox 2021-10-25 Answered

### Random variable X and Y have the joint PDF $$f_{XY}(x,y)=\begin{cases}c,\ x\geq 0,y\geq 0,(x^{2}+y)\leq 1,\\0,\ \ \ \ \ otherwise \end{cases}$$ Find the marginal PDF $$\displaystyle{{f}_{{{X}}}{\left({x}\right)}}$$. Dolly Robinson 2021-10-23 Answered

### Let $$\displaystyle{X}_{{{1}}},{X}_{{{2}}},\ldots,{X}_{{{n}}}$$ be n independent random variables each with mean 100 and standard deviation 30. Let X be the sum of these random variables. Find n such that $$\displaystyle{P}{r}{\left({X}{>}{2000}\right)}\geq{0.95}$$. Wierzycaz 2021-10-23 Answered

### Random variable X and Y have the joint PDF $$f_{XY}(x,y)=\begin{cases}c,\ x\geq 0,y\geq 0,(x^{2}+y)\leq 1,\\0,\ \ \ \ \ otherwise \end{cases}$$ Find the constant c. Ava-May Nelson 2021-10-22 Answered

### Two random variables X and Y with joint density function given by: $$f(x,y)=\begin{cases}\frac{1}{3}(2x+4y)& 0\leq x,\leq 1\\0 & elsewhere\end{cases}$$ Find $$\displaystyle{P}{\left({x}{<}{\frac{{{1}}}{{{3}}}}\right)}$$ Daniaal Sanchez 2021-10-22 Answered

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