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.

options a,b,c are the right answer.

step-by-step explanation:

a linear parent function is always represented as y = x

if we write this function in the form of y=mx+c

⇒

or  

now if we plot a graph we will find these characteristics:

1) y intercept of the graph is zero so its a straight line passing through origin.

2) as we can see in both the forms of function written, values of x and y may be either positive or negative for the positive slope means points on the graph are either in first quadrant or in third one.

3) it's slope is one.

the correct answer is you spend $55.78 more in a brand store that buy ing in a normal store.

step-by-step explanation:

brand = spend   $ 135.85 total

store = spend $80.07 total