Consider the following joint probability density function of the random variables X and Y:
f(x, y)= {6y 0 o otherwise}
(1) Find the marginal distribution of X and erify that it is a valid density function.
(2) What is the probability that proportion Y is less than 0.5, given that X is 0.7.

Step-by-step explanation:

Given that a joint probability density function of the random variables X and Y: is

To find the marginal distribution of x

1) To find marginal distribution of x, we integrate with respect to y the region of y.

Here region of y is 0<y<x

So pdf of X =

2) P(y<0.5/x=0.7)

X is having a continuous pdf and hence P(x=0.7) =0

(For any continuous distribution at a particular point prob is 0)

So we find that P(y<0.5/x=0.7) does not exist.

75

step-by-step explanation:

you do x-29=46 (the number of cantaloupes sold)

in order to find x, you have to find what minus 29 equals 46, meaning you'd have to add 29 to 46.

29+46=75

if you replace x with 75, the equation looks like:

75-29=46

x=75

14.3

step-by-step explanation:

add all the numbers together.

9 + 12 + 15 + 16 + 17 + 17 = 86

now, divide 86 by how many numbers we have: 6.

86 / 6 = 14.3