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15. When a fire occurs, the model for fire damage in a particular property is based...
The model for the amount of damage to a particular property during a one-month period is as follo...
The model for the amount of damage to a particular property during a one-month period is as follows: there is a .99 probability of no damage, there is a.01 probability that damage will occur, and if damage does occur, it is uniformly distributed between 1000 and 2000. An insurance policy pays the amount of damage up to a policy limit of 1500. It is later found that the original model for damage when damage does occur was incorrect, and should...
Suppose that random variables X and Y have a joint uniform distribution over the following range:...
Suppose that random variables X and Y have a joint uniform distribution over the following range: 0 < y < x/3 < 1. a) Find the probability that Y > 1/2 b) Find the marginal density function fx(x)
Dependent Variable: Y $1000 fire damage &n...
Dependent Variable: Y $1000 fire damage Analysis of Variance Sum of Mean Source DF Squares Square F Value Pro Model 1 841.76636 841.76636 156.886 0.0001 Error 13 69.75098 5.36546 Total(Adjusted) 14 911.51733 Root MSE 2.31635 R-square 0.9235 Dep Mean 26.41333 Adj R-sq 0.9176 C.V. 8.76961 Parameter Estimates Parameter Standard T for H0: Variable Estimate Error Parameter=0 Prob > |T| INTERCEPT 10.277929 1.42027781 7.237 0.0001 X 4.919331 0.39274775 12.525 0.0001 Dep Actual Predicted 95% LCL 95% UCL 95% LCL 95% Obs ...
Exercise 10.33. Let (X,Y) be uniformly distributed on the triangleD with vertices (1,0), (2,0) and (0,1), as in Example...
Exercise 10.33. Let (X,Y) be uniformly distributed on the
triangleD with vertices (1,0), (2,0) and (0,1), as in Example
10.19. (a) Find the conditional probability P(X ≤ 1 2|Y =y). You
might first deduce the answer from Figure 10.2 and then check your
intuition with calculation. (b) Verify the averaging identity for
P(X ≤ 1 2). That is, check that P(X ≤ 1 2)=:∞ −∞ P(X ≤ 1 2|Y
=y)fY(y)dy.
Example 10.19. Let (X, Y) be uniformly distributed on the...
7. The random variables X and Y have joint probability density function f given by 1...
7. The random variables X and Y have joint probability density function f given by 1 for x > 0, |y| 0 otherwise. 1-x, Below you find a diagram highlighting the (r, y) pairs for which the pdf is 1 (a) Calculate the marginal probability density function fx of X (b) Calculate the marginal cumulative distribution function Fy of Y (c) Are X and Y independent? Explain.
7. The random variables X and Y have joint probability density function f given by 1...
7. The random variables X and Y have joint probability density function f given by 1 for x > 0, |y| 0 otherwise. 1-x, Below you find a diagram highlighting the (r, y) pairs for which the pdf is 1 (a) Calculate the marginal probability density function fx of X (b) Calculate the marginal cumulative distribution function Fy of Y (c) Are X and Y independent? Explain.
2. Suppose a fire insurance company wants to relate the amount of fire damage in major...
2. Suppose a fire insurance company wants to relate the amount of fire damage in major residential fires to the distance between the burning house and the nearest fire station. A random sample of 15 fires in a large suburb is selected. The amount of damage (thousands of dollars) and the distance (miles) between the fire and the nearest fire station are recorded for each fire. The following simple linear regression model was used: Fire Damagei=B0+B1(Distance from Fire Station)i+Ei Coefficients...
1. Suppose that X and Y are random variables that can only take values in the intervals 0 X 2 and...
1. Suppose that X and Y are random variables that can only take values in the intervals 0 X 2 and 0 Y 3 2. Suppose also that the joint cumulative distribution function (cdf) of X and Y, for 0 < 2 and 03 y 3 2, is as follows: Fy). 16 [5] (a) Determine the marginal cdf Fx(x) of X and the marginal cdf Fy () of Y [5] (b) Determine the joint probability density function (pdf) f(x, y)...
Need help with question 2 (not question 1) 1. Suppose that (X,Y) is uniformly distributed over...
Need help with question 2 (not question
1)
1. Suppose that (X,Y) is uniformly distributed over the region {(x, y): 0 < \y< x < 1}. Find: a) the joint density of (X, Y); b) the marginal densities fx(x) and fy(y). c) Are X and Y independent? d) Find E(X) and E(Y). 2. Repeat Exercise 1 for (X,Y) with uniform distribution over {(x, y): 0 < \x]+\y< 1}.
The model for the amount of damage to a particular property during a one-month period is as follows: there is a .99 probability of no damage, there is a.01 probability that damage will occur, and if damage does occur, it is uniformly distributed between 1000 and 2000. An insurance policy pays the amount of damage up to a policy limit of 1500. It is later found that the original model for damage when damage does occur was incorrect, and should...
Exercise 10.33. Let (X,Y) be uniformly distributed on the
triangleD with vertices (1,0), (2,0) and (0,1), as in Example
10.19. (a) Find the conditional probability P(X ≤ 1 2|Y =y). You
might first deduce the answer from Figure 10.2 and then check your
intuition with calculation. (b) Verify the averaging identity for
P(X ≤ 1 2). That is, check that P(X ≤ 1 2)=:∞ −∞ P(X ≤ 1 2|Y
=y)fY(y)dy.
Example 10.19. Let (X, Y) be uniformly distributed on the...
7. The random variables X and Y have joint probability density function f given by 1 for x > 0, |y| 0 otherwise. 1-x, Below you find a diagram highlighting the (r, y) pairs for which the pdf is 1 (a) Calculate the marginal probability density function fx of X (b) Calculate the marginal cumulative distribution function Fy of Y (c) Are X and Y independent? Explain.
7. The random variables X and Y have joint probability density function f given by 1 for x > 0, |y| 0 otherwise. 1-x, Below you find a diagram highlighting the (r, y) pairs for which the pdf is 1 (a) Calculate the marginal probability density function fx of X (b) Calculate the marginal cumulative distribution function Fy of Y (c) Are X and Y independent? Explain.
1. Suppose that X and Y are random variables that can only take values in the intervals 0 X 2 and 0 Y 3 2. Suppose also that the joint cumulative distribution function (cdf) of X and Y, for 0 < 2 and 03 y 3 2, is as follows: Fy). 16 [5] (a) Determine the marginal cdf Fx(x) of X and the marginal cdf Fy () of Y [5] (b) Determine the joint probability density function (pdf) f(x, y)...
Need help with question 2 (not question
1)
1. Suppose that (X,Y) is uniformly distributed over the region {(x, y): 0 < \y< x < 1}. Find: a) the joint density of (X, Y); b) the marginal densities fx(x) and fy(y). c) Are X and Y independent? d) Find E(X) and E(Y). 2. Repeat Exercise 1 for (X,Y) with uniform distribution over {(x, y): 0 < \x]+\y< 1}.
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