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Statistics I20755 marksNumerical: joint probability density functionJoint probability distribution of two random variables

If two random variables have the joint probability density function

$f(x,y) = \begin{cases} k e^{-(x+y)}, & 0 < x < \infty, 0 < y < \infty \\ 0, & \text{otherwise} \end{cases}$

Find (i) constant $k$ (ii) conditional probability density function of $X$ given $Y$ (iii) Var $(3X + 2Y)$ . [5]

If two random variables have the joint probability density function

$$f(x,y) = \begin{cases} k e^{-(x+y)}, & 0 < x < \infty, 0 < y < \infty \ 0, & \text{otherwise} \end{cases}$$

Find (i) constant $k$ (ii) conditional probability density function of $X$ given $Y$ (iii) Var$(3X + 2Y)$. [5]

Joint PDF: $f(x,y) = \begin{cases} k\,e^{-(x+y)}, & 0<x<\infty,\ 0<y<\infty \\ 0, & \text{otherwise} \end{cases}$ Find: (i) constant $k$ , (ii) conditional PDF of $X$ given $Y$ , (iii) $\text{Var}(3X+2Y)$ . --- $\int0^\infty\int0^\infty k\,e^{-(x+y)}\,dx\,dy = 1$ Separating: $$k\left(\int0^\inft...

Joint PDF: $$f(x,y) = \begin{cases} k,e^{-(x+y)}, & 0<x<\infty,\ 0<y<\infty \ 0, & \text{otherwise} \end{cases}$$ Find: (i) constant $k$, (ii) conditional PDF of $X$ given $Y$, (iii) $\text{Var}(3X+2Y)$. --- $$\int0^\infty\int0^\infty k,e^{-(x+y)},dx,dy = 1$$ Separating: $$k\left(\int0^\inft...

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If two random variables have the joint probability density function Find (i) constant k (ii) conditional probability density function of X given Y (iii) Var(3X + 2Y).