Question

Consider independent random variables X and Y , such that X has mean 2 and standard deviation 4, and Y has mean 1 and standard deviation 9. Find the mean and standard deviation of the following random variables. a) 3X b) Y + 6 c) X + Y d) X − Y e) X1 + X2, where X1, X2 are independent copies of X.

Answer #1

Given independent random variables with means and standard
deviations as shown, find the mean and standard deviation of each
of these variables:
Mean
SD
a) 4X
b) 4Y+3
c) 2X+5Y
X
70
14
d) 5X−4Y
e) X1+X2
Y
10
5
a) Find the mean and standard deviation for the random variable
4X.
E(4X)=_____________
SD(4X)=_______________
(Round to two decimal places as needed.)
b) Find the mean and standard deviation for the random variable
4Y+3.
E(4Y+3)= ________________
SD(4Y+3)= _____________________
(Round to...

Let X and Y be independent and identically
distributed random variables with mean μ and variance
σ2. Find the following:
a) E[(X + 2)2]
b) Var(3X + 4)
c) E[(X - Y)2]
d) Cov{(X + Y), (X - Y)}

Let Y be the liner combination of the independent random
variables X1 and X2 where Y = X1 -2X2
suppose X1 is normally distributed with mean 1 and standard
devation 2
also suppose the X2 is normally distributed with mean 0 also
standard devation 1
find P(Y>=1) ?

X and Y are independent random variables. The mean and variance
of X are 2 and 1 respectively. The mean and variance of Y are 3 and
2 respectively. Which of the statements below about the random
variable X-Y is true?
a. X-Y~Normal(-1,1)
b. X-Y~Normal(1,3)
c. X-Y has mean -1 and variance 3.
d. X-Y has mean 5 and variance 3.

The expected values, variances and standard Deviatiations for
two random variables X and Y are given in the following table
Variable
expected value
variance
standard deviation
X
20
9
3
Y
35
25
5
Find the expected value and standard deviation of the following
combinations of the variable X and Y. Round to nearest whole
number.
E(X+10) = ,
StDev(X+10) =
E(2X) = ,
StDev(2X) =
E(3X-2) = ,
StDev(3X-2) =
E(3X +4Y) = ,
StDev(3X+4Y) =
E(X-2Y) = ,
StDev(X-2Y) =

Suppose X1, X2, X3, and
X4 are independent and identically distributed random
variables with mean 10 and variance 16. in addition, Suppose that
Y1, Y2, Y3, Y4, and
Y5are independent and identically distributed random
variables with mean 15 and variance 25. Suppose further that
X1, X2, X3, and X4 and
Y1, Y2, Y3, Y4, and
Y5are independent. Find Cov[bar{X} + bar{Y} + 10,
2bar{X} - bar{Y}], where bar{X} is the sample mean of
X1, X2, X3, and X4 and
bar{Y}...

Continuous random variables X1 and X2 with joint density
fX,Y(x,y) are independent and identically distributed with expected
value μ.
Prove that E[X1+X2] = E[X1] +E[X2].

Let X and Y be two independent random variables with
μX =E(X)=2,σX =SD(X)=1,μY =2,σY =SD(Y)=3.
Find the mean and variance of
(i) 3X
(ii) 6Y
(iii) X − Y

1.) Consider two independent discrete random variables X and Y
with V(X)=2 and V(Y)=5. Find V(4X-8Y-9).
2.) Consider two independent discrete random variables X and Y
with SD(X)=16 and SD(Y)=9. Find SD(5X-2Y-13). (Round your answer to
1 place after the decimal point).
3.)Consider two discrete random variables X and Y with V(X)=81
and V(Y)=36 and correlation ρ=0.7. Find V(X-Y). (Round your answer
to 1 digit after the decimal point).

1.suppose that Y1 and Y2 are independent random variables
2.suppose that Y1 and Y2each have a mean of A and a variance of
B
3.suppose X1 and X2 are related to Y1 and Y2 in the following
way:
X1=C/D x Y1
X2= CY1+CY2
4.suppose A, B, C, and D are constants
What is the expected value of the expected value of X1 given
X2{E [E (X1 | X2)]}?
What is the expected value of the expected value of X2 given...

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