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Random Variable $X$ and $Y$ has a joint probability density function. Find $f_X (x | y)$

A continuous random variable X has probability density functionFind Joint Probability Density FunctionDeriving Joint probability density functionsProblem of joint density function of random variable $(X,Y)$.How to find the joint distribution and joint density functions of two random variables?Joint Density Function Problem Find Conditional ProbabilityFind the probability density functions of $X$ and $Y$Random Variable X and Y has a joint probability density function. Find $P(x | y)(x | y)$Random Variable X and Y has a joint probability density function.Find the density function of a random variable that depends on two other random variables with a given joint distribution.

1

$begingroup$

Random Variable X and Y has a joint probability density function.

$$f_X, Y (x, y) =begincases
c(x + 3y)& 5 leq x leq y, 6 leq y leq10\
0 & textotherwise \
endcases
$$

(a) Find $f_X (x | y)$

(b) $P(x leq 5 | Y = 9)$

---

My attempt:

$f_X (x | y) = fracf_X, Y(x, y)f_Y(y)$

$$f_Y(y) = cint_5^y(x+3y)dx = c/2 (-25 - 30 y + 7 y^2)$$

for $f_Y(y)$ has support $6 leq y leq 10$, 0 otherwise

$$f_X (x | y) = frac0.5c(x+3y)(-25 - 30 y + 7 y^2)$$

$f_X (x | y)$ has support the same as the joint probability function

(b)

$f_X (x | y = 9) = fracx+27272$

$$P(x leq 5 | Y = 9) = int_5^? f_X (x | y = 9)dx = $$

Not sure

probability

share|cite|improve this question

edited Mar 14 at 6:17

Rócherz

2,9863821

asked Jul 19 '18 at 7:39

Bas basBas bas

49512

$endgroup$

• 
  
  
  

  
  1
  

  
  
  
  
  
  

  
  $begingroup$
  Replace $?$ by $5$ and the answer is $0$.
  $endgroup$
  – Piyush Divyanakar
  Jul 19 '18 at 10:15
  

  
  
  
  

add a comment | 

1

$begingroup$

Random Variable X and Y has a joint probability density function.

$$f_X, Y (x, y) =begincases
c(x + 3y)& 5 leq x leq y, 6 leq y leq10\
0 & textotherwise \
endcases
$$

(a) Find $f_X (x | y)$

(b) $P(x leq 5 | Y = 9)$

---

My attempt:

$f_X (x | y) = fracf_X, Y(x, y)f_Y(y)$

$$f_Y(y) = cint_5^y(x+3y)dx = c/2 (-25 - 30 y + 7 y^2)$$

for $f_Y(y)$ has support $6 leq y leq 10$, 0 otherwise

$$f_X (x | y) = frac0.5c(x+3y)(-25 - 30 y + 7 y^2)$$

$f_X (x | y)$ has support the same as the joint probability function

(b)

$f_X (x | y = 9) = fracx+27272$

$$P(x leq 5 | Y = 9) = int_5^? f_X (x | y = 9)dx = $$

Not sure

probability

share|cite|improve this question

edited Mar 14 at 6:17

Rócherz

2,9863821

asked Jul 19 '18 at 7:39

Bas basBas bas

49512

$endgroup$

• 
  
  
  

  
  1
  

  
  
  
  
  
  

  
  $begingroup$
  Replace $?$ by $5$ and the answer is $0$.
  $endgroup$
  – Piyush Divyanakar
  Jul 19 '18 at 10:15
  

  
  
  
  

add a comment | 

$begingroup$

Random Variable X and Y has a joint probability density function.

$$f_X, Y (x, y) =begincases
c(x + 3y)& 5 leq x leq y, 6 leq y leq10\
0 & textotherwise \
endcases
$$

(a) Find $f_X (x | y)$

(b) $P(x leq 5 | Y = 9)$

---

My attempt:

$f_X (x | y) = fracf_X, Y(x, y)f_Y(y)$

$$f_Y(y) = cint_5^y(x+3y)dx = c/2 (-25 - 30 y + 7 y^2)$$

for $f_Y(y)$ has support $6 leq y leq 10$, 0 otherwise

$$f_X (x | y) = frac0.5c(x+3y)(-25 - 30 y + 7 y^2)$$

$f_X (x | y)$ has support the same as the joint probability function

(b)

$f_X (x | y = 9) = fracx+27272$

$$P(x leq 5 | Y = 9) = int_5^? f_X (x | y = 9)dx = $$

Not sure

probability

share|cite|improve this question

edited Mar 14 at 6:17

Rócherz

2,9863821

asked Jul 19 '18 at 7:39

Bas basBas bas

49512

$endgroup$

share|cite|improve this question

edited Mar 14 at 6:17

Rócherz

2,9863821

asked Jul 19 '18 at 7:39

Bas basBas bas

49512

share|cite|improve this question

edited Mar 14 at 6:17

Rócherz

2,9863821

asked Jul 19 '18 at 7:39

Bas basBas bas

49512

edited Mar 14 at 6:17

Rócherz

2,9863821

edited Mar 14 at 6:17

Rócherz

2,9863821

asked Jul 19 '18 at 7:39

Bas basBas bas

49512

asked Jul 19 '18 at 7:39

Bas basBas bas

49512