Q: Assistance in understanding and solving this example from Probability and Statistical (Conditional Distributions) with the steps of the solution to better understand, thanks.
**Please give the step by steps with details to completely see how the solution came about.
1) Suppose X and Y both take values in [0,1] with joint probability density f(x,y) = 4xy.
a) Find fx(x) and fy(y), the marginal probability density functions.
b) Are the two random variables independent? Why or why not?
c) Compute the means and variances of X and Y.
d) Find P(X
Y).
1)
a)
similarly
b)
Yes , two variables are independent as
f(x,y) = f(x) f(y)
c)
Var(X) = E(X^2) - (E(X))^2
hence
Var(X) = 1/2 - (2/3)^2
= 0.05555
E(Y) = E(X) = 2/3
Var(Y) = Var(X) = 0.05555 {X and Y are symmetric}
d)
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Q: Assistance in understanding and solving this example from Probability and Statistical (Conditional Distributions) with the...
Q: Asking for assistance in understanding and solving this
example on Probability and Statistical with the steps of the
solution to better understand, thanks.
**Please give the step by steps with details to
completely see how the solution came about.
1) Let the joint pmf of X and Y be defined by: f(x,y) =
(x+y)/(33), x=1,2, y=1,2,3.
(a) Find fx(x), the marginal pmf
of X.
(b) Find fy(y), the marginal pmf
of Y.
(c) Find P(X >...
Q: Assistance in understanding and solving this example from
Probability and Statistical (Conditional Distributions) with the
steps of the solution to better understand, thanks.
**Please give the step by steps with details to
completely see how the solution came about.
1) Let X and Y have the joint pmf: f(x,y) =
(x+2y)/33, x = 1,2 y = 1,2,3.
a) Display the joint pmf and the marginal pmfs on a graph.
b) Find g(x
y) and draw a figure depicting the...
Q: Assistance in understanding and solving this example on Probability and Statistical with the steps of the solution to better understand, thanks. **Please give the step by steps with details to completely see how the solution came about. 1) Let be random variables of the continuous type have the joint p.d.f. f(x,y)= 2, 0≤y≤ x≤1. (a). Draw a graph that illustrates the domain (support) of this p.d.f. (b). Find marginal pdf of X, fX(x), μXand σ2X (c). Find the marginal...
Q: Asking for assistance in understanding and solving this
example on Probability and Statistical with the steps of the
solution to better understand, thanks.
**Please give the step by steps with details to
completely see how the solution came about.
1) The joint pmf of X and Y is given by: f(x,y) =
c(x+1)(4-x)(y+1)(3-y), x=0,1,2,3 y=0,1,2 with y
x.
(a) Compute Cov(X,Y). *In using this
(x)(y)f(x,y).
Q: Help in understanding and solving this example from
Probability and Statistical (Conditional Distributions) with the
steps of the solution to better understand, thanks.
**Please give the step by steps with details to
completely see how the solution came about.
1) Let X and Y have the joint p.m.f: f(x,y) =
(x+2y)/33, x = 1,2 y = 1,2,3.
a) Display the joint p.m.f and the marginal p.m.f.s on a
graph.
b) Find g(x
y) and draw a figure depicting the...
Q: Asking for assistance in understanding and solving this
example on Probability and Statistical with the steps of the
solution to better understand, thanks.
**Please give the step by steps with details to
completely see how the solution came about.
1) The joint pmf of X and Y is given by: f(x,y) =
c(x+1)(4-x)(y+1)(3-y), x=0,1,2,3 y=0,1,2 with y
x.
(a) Find the value of c.
(b) Sketch the support of X and Y.
(c) Record the marginal...
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Q: Help to understand clearly and solve this example from
Probability and Statistical Inference with the
steps of the solution to better understand, thanks.
**Please give the step by step with details to
completely see how the solution came about, plenty of
thanks.
1) Let Y be b(100,p). To test H0:p = 0.09 against
H1:p > 0.09, we reject H0 and accept
H1 if and only if Y<= 5. Determine the significance
level of the test.
Note: Please use Normal...