Question
In: Statistics and Probability
Let Y = X1 + X2 + 2X3 represent the perimeter of an isosceles trapezoid, where...
Let Y = X1 + X2 + 2X3 represent the perimeter of an isosceles trapezoid, where X1 is
normally distributed with a mean of 113 cm and a standard deviation of 5 cm, X2 is normally
distributed with a mean of 245 cm and a standard deviation of 10 cm, and X3 is normally
distributed with a mean of 98 cm and a standard deviation of 2 cm.
1. Find the mean perimeter of the trapezoid.
2. Suppose X1;X2; and X3 are independent of each other. Find the variance of the
perimeter of the trapezoid.
3. Suppose that the covariance between X1 and X2 is 35, but X3 is independent of both
X1 and X2. Find the variance of the perimeter of the trapezoid.
Solutions
orchestra answered 2 years agoRelated Solutions
Let Y = X1 + X2 + 2X3 represent the perimeter of an isosceles trapezoid, where...
Let Y = X1 + X2 + 2X3 represent the perimeter of an isosceles
trapezoid, where X1 is normally distributed with a mean of 113 cm
and a standard deviation of 5 cm, X2 is normally distributed with a
mean of 245 cm and a standard deviation of 10 cm, and X3 is
normally distributed with a mean of 98 cm and a standard deviation
of 2 cm.
1. Find the mean perimeter of the trapezoid.
2. Suppose X1, X2,...
x1 + x2 - 2x4 = 2 x1 + x2 + 2x3 + 6x4 + x5...
x1 + x2 - 2x4 = 2
x1 + x2 + 2x3 + 6x4 + x5 = 8
−2x1 - 2x2 + x3 + 8x4 = −1
3x3 + 12x4 + 2x5 = 9
Let the linear system be given.
a. Find the reduced row eelon form of the combined
matrix (augmented matrix) of the system.
b. Is the system consistent? If the system is
consistent, find the overall solution of the system.
c. Do all the solutions of the...
Probabilities Compute P(X1 + 2X2 -2X3 > 7) , where X1, X2, X3 are iid random...
Probabilities
Compute P(X1 + 2X2 -2X3 > 7)
, where X1, X2, X3 are iid random
variables with common distribution N(1,4). You must give the
numerical answer.
Specify and show any formulas used for E, P, and Var
for example Var( X1 + 2X2 -2X3)
= 4 + 22(4) + (-2)2(4) = 35. Please specify
how all the individual numbers where obtained and the formula
used.
(a) Let x1 and x2 be normal goods. Graphically, represent the effect of an increase in...
(a) Let x1 and x2 be normal goods. Graphically, represent the
effect of an increase in the price level of x2. Show the Slutsky
substitution and income effects on a clearly labelled diagram. (b)
On a separate graph, show what would happen if x2 is now a Giffen
good. Show the (Slutsky) substitution and income effects clearly
and explain which effect outweighs the other. Note: For both parts
x1 should be on the x-axis Assume the utility function to be...
Sophie's utility function is given as U = 2(x1)^(1/2) + 8(x2) where x1 and x2 represent...
Sophie's utility function is given as U = 2(x1)^(1/2) + 8(x2)
where x1 and x2 represent the two goods Sophie consumes. Sophie's
income is $3400 and the prices are given as x1 = $2 and x2 =
$160
a) derive & represent in two separate diagrams the demand
for x1 and x2 ( for any income and prices)
b) If Sophie's income is increased to $6600, what is the income
effect on x1? Is x2 a normal good? Justify your...
Let X1, X2, . . . , Xn represent a random sample from a Rayleigh distribution...
Let X1, X2, . . . , Xn represent a random sample from a Rayleigh distribution with pdf
f(x; θ) = (x/θ) * e^x^2/(2θ) for x > 0
(a) It can be shown that E(X2 P ) = 2θ. Use this fact to construct an unbiased estimator of θ based on n i=1 X2 i .
(b) Estimate θ from the following n = 10 observations on vibratory stress of a turbine blade under specified conditions:
16.88 10.23 4.59 6.66...
Let T(x1, x2) = (-x1 + 3x2, x1 - x2) be a transformation. a) Show that...
Let T(x1, x2) = (-x1 + 3x2, x1 - x2) be a transformation.
a) Show that T is invertible.
b)Find T inverse.
Let the utility function be given by u(x1, x2) = √x1 + x2. Let m be...
Let the utility function be given by
u(x1, x2) = √x1 + x2.
Let m be the income of the consumer, P1 and P2 the prices of good 1
and good 2, respectively.
To simplify, normalize the price of good 1, that is P1 = £1.
(a) Write down the budget constraint and illustrate the set of
feasible bundles using a figure.
(b) Suppose that m = £100 and that P2 = £10. Find the optimal
bundle for the consumer....
Case Y X1 X2
Case
Y
X1
X2
X3
X4
X5
X6
1
43
45
92
61
39
30
51
2
63
47
73
63
54
51
64
3
71
48
86
76
69
68
70
4
61
35
84
54
47
45
63
5
81
47
83
71
66
56
78
6
43
34
49
54
44
49
55
7
58
35
68
66
56
42
67
8
74
41
66
70
53
50...
Consider a capital budgeting formulation where the binary variables x1 and x2 are used to represent...
Consider a capital budgeting formulation where the binary
variables x1 and x2 are used to represent the
acceptance (xi = 1) or rejection (xi = 0) of
each alternative. Which of the following constraints shows that
investing in alternative 1 is contingent upon investing in
alternative 2?
a. x1 + x2 ≤ 1
b. x1 + x2 ≥ 1
c. x1 + x2 ≥ 1
d. x1 ≥ x2
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