Question

1. The amount of kerosene, in thousands of liters in a tank at the beginning of the day is a random amount Y from which a random amount X is sold during that day. Suppose that the tank is not resupplied during the day, so $x le y$, and assume that the joint density function of the variables is $egin{aligned} f(x,y) = egin{cases} 2 & ext{if } 0 < x le y < 1\ 0 & ext{otherwise} end{cases} end{aligned}$ (a) Determine if X and Y are independent. (b) Find $P(frac{1}{4} < X < frac{1}{2} | Y = frac{3}{4})$. (c) Find $Cov(X, Y)$.

          1.
The amount of kerosene, in thousands of liters in a tank at the beginning
of the day is a random amount Y from which a random amount X is sold during that
day. Suppose that the tank is not resupplied during the day, so $x le y$, and assume that
the joint density function of the variables is
$egin{aligned}
f(x,y) = egin{cases} 2 & 	ext{if } 0 < x le y < 1\ 0 & 	ext{otherwise} end{cases}
end{aligned}$
(a) Determine if X and Y are independent.
(b) Find $P(frac{1}{4} < X < frac{1}{2} | Y = frac{3}{4})$.
(c) Find $Cov(X, Y)$.

$1. The amount of kerosene, in thousands of liters in a tank at the beginning of the day is a random amount Y from which a random amount X is sold during that day. Suppose that the tank is not resupplied during the day, so x le y, and assume that the joint density function of the variables is eginaligned f(x,y) = egincases 2 extif 0 < x le y < 1 0 extotherwise endcases endaligned (a) Determine if X and Y are independent. (b) Find P(frac14 < X < frac12 | Y = frac34). (c) Find Cov(X, Y).$

Added by Brian C.

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