The joint density function of two continuous random variables X and Y is: f(x,y)=f(x,y)={cx2e−y31&lt;x&lt;6,2&lt;y&lt;4=00otherwise Draw the integration boundaries and write the integration only for P(X+Y≤6)

Integration boundaries for X+Y≤6: X: 1 to 6-y Y: 2 to 4 Integration: P(X+Y≤6)=∫y=24∫x=16−y0.0186x2e−y3dxdy =0.0186∫y=24e−y3[x33]16−ydy =0.0186∫24e−y3[(6−y)33−13]dy =0.0062∫24e−y3[(6−y)3−1]dy =0.0062⋅24.0489 =0.1491

Answered: "The joint density function of two continuous random..."

College
Statistics and Probability
College Statistics
Random variables

bobbie71G

Answered question

2021-06-05

The joint density function of two continuous random variables X and Y is:
$f (x, y) = f (x, y) = {\begin{cases} c x^{2} e^{\frac{- y}{3}} & 1 < x < 6, 2 < y < 4 = 0 \\ 0 & o t h e r w i s e \end{cases}$
Draw the integration boundaries and write the integration only for $P (X + Y \leq 6)$

Answer & Explanation

dieseisB

Skilled2021-06-06Added 85 answers

Integration boundaries for $X + Y \leq 6$ :
X: 1 to 6-y
Y: 2 to 4
Integration:
$P (X + Y \leq 6) = \int_{y = 2}^{4} \int_{x = 1}^{6 - y} 0.0186 x^{2} e^{\frac{- y}{3}} d x d y$
$= 0.0186 \int_{y = 2}^{4} e^{\frac{- y}{3}} [\frac{x^{3}}{3}]_{1}^{6 - y} d y$
$= 0.0186 \int_{2}^{4} e^{\frac{- y}{3}} [\frac{(6 - y)^{3}}{3} - \frac{1}{3}] d y$
$= 0.0062 \int_{2}^{4} e^{\frac{- y}{3}} [(6 - y)^{3} - 1] d y$
$= 0.0062 \cdot 24.0489$
=0.1491

Do you have a similar question?

Recalculate according to your conditions!

New Questions in College Statistics

The product of the ages, in years, of three (3) teenagers os 4590. None of the have the sane age. What are the ages of the teenagers???
Use the row of numbers shown below to generate 12 random numbers between 01 and 99
78038 18022 84755 23146 12720 70910 49732 79606
Starting at the beginning of the row, what are the first 12 numbers between 01 and 99 in the sample?
How many different 10 letter words (real or imaginary) can be formed from the following letters
H,T,G,B,X,X,T,L,N,J.
Is every straight line the graph of a function?
For the 1s orbital of the Hydrogen atom, the radial wave function is given as: $R (r) = \frac{1}{\sqrt{π}} (\frac{1}{a_{O}})^{\frac{3}{2}} e^{\frac{- r}{a_{O}}}$ (Where $a_{O} = 0.529$ ∘A)
The ratio of radial probability density of finding an electron at $r = a_{O}$ to the radial probability density of finding an electron at the nucleus is given as ( $x . e^{- y}$ ). Calculate the value of (x+y).
Find the sets $A$ and $B$ if $\frac{A}{B} = (1, 5, 7, 8), \frac{B}{A} = (2, 10)$ and $A \cap B = (3, 6, 9)$ . Are they unique?
What are the characteristics of a good hypothesis?
If x is 60% of y, find $\frac{x}{y - x}$ .
A) $\frac{1}{2}$
B) $\frac{3}{2}$
C) $\frac{7}{2}$
D) $\frac{5}{2}$
The numbers of significant figures in $9.1 \times 10^{- 31} k g$ are:
A)Two
B)Three
C)Ten
D)Thirty one
What is positive acceleration?
Is power scalar or vector?
What is the five-step process for hypothesis testing?
How to calculate Type 1 error and Type 2 error probabilities?
How long will it take to drive 450 km if you are driving at a speed of 50 km per hour?
1) 9 Hours
2) 3.5 Hours
3) 6 Hours
4) 12.5 Hours
What is the square root of 106?

Didn't find what you were looking for?