Find the distribution of R = A sin θ , where A is a fixed constant and θ is uniformly distributed on ( − π 2 , π 2 ) . Such a random variable R arises in the theory of ballistics. If a projectile is fired from the origin at an angle α from the earth with a speed v. then the point R at which it returns to the earth can be expressed as R = ( v 2 g ) sin 2 α , where g is the gravitational constant, equal to 980 centimeters per second squared.
Find the distribution of R = A sin θ , where A is a fixed constant and θ is uniformly distributed on ( − π 2 , π 2 ) . Such a random variable R arises in the theory of ballistics. If a projectile is fired from the origin at an angle α from the earth with a speed v. then the point R at which it returns to the earth can be expressed as R = ( v 2 g ) sin 2 α , where g is the gravitational constant, equal to 980 centimeters per second squared.
Find the distribution of
R
=
A
sin
θ
, where A is a fixed constant and
θ
is uniformly distributed on
(
−
π
2
,
π
2
)
. Such a random variable R arises in the theory of ballistics. If a projectile is fired from the origin at an angle
α
from the earth with a speed v. then the point R at which it returns to the earth can be expressed as
R
=
(
v
2
g
)
sin
2
α
, where g is the gravitational constant, equal to 980 centimeters per second squared.
Let X and Y be random variables for which the joint PDF is as follows:
(8xy
f(x, y) = {8xy
for 0
C2. Let X and Y be random variables, and let a and b be constants.
(a) Starting from the definition of covariance, show that Cov(aX, Y): = a Cov(X, Y). You may find
it helpful to remember that if EX = µx, then EaX = αμχ·
(b) Show that Cov(X + b, Y) = Cov(X, Y).
Now let X, Y, Z be independent random variables with common variance o².
(c) Find the value of Corr(2X - 3Y + 4, 2Y – Z - 1). You may use any facts about covariance from
the notes, including those from parts (a) and (b) of this question, provided you state them clearly.
I send for 3.question but you answered only a and b
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