11. The marginal density functions for independent random variables X and Y are g(x) andh(y). Find the joint probability density function f(x, y) for the independent randomvariables X and Y. Your answer should be a piecewise function.= { x + /20g(x):0 < x < 1elsewhereh(y)=+00 < y < 1elsewhere 8. The density function for the random variable X is f(x). Find E(3X - 1).) = √(= (2x + 1(2x + 1)E(3X - 1) =f(x) =1 < x < 20 elsewhere

Answered: Image /qna-images/answer/2f9e1d5d-ec9e-432a-b296-2feae6aeb5fa.jpg

Answered: 11. The marginal density functions for…

Algebra & Trigonometry with Analytic Geometry

13th Edition

ISBN:9781133382119

Author:Swokowski

Publisher:Swokowski

Chapter5: Inverse, Exponential, And Logarithmic Functions

Section5.2: Exponential Functions

Problem 58E

See similar textbooks

Similar questions

Q4) The probability mass function of Y is f(y) = y/6 for y=1,2,3,4. Find the variance of Y.
3. Let X be a continuous random variable on the interval [0, 1] having cdf Fx(x) = 3x² − 2x³. Let W = 4 + 3X. (a) What is the range of W? (b) Find a formula for Fw(w). (c) Find a formula for fw(w).
X and Y are two independent random variables with fy (x) eX-u (x) and fy (V) = e. u (y). Find the mean of the random variable Z= X - Y for X> Y for. X< Y
Suppose that Y₁ and Y₂ are uniformly distributed over the triangle shaded in the accompanying figure. 3₂ (0, 1) (-1,0) (a) Find Cov(Y₁ Y₂). Cov(Y₁, Y₂) = (b) Are Y₁ and Y₂ independent? Yes O No (1, 0) (c) Find the coefficient of correlation for Y₁ and Y₂. P= y/₁ (d) Does your answer to part (b) lead you to doubt your answer to part (a)? Why or why not? O Even though Cov(Y₁Y₂) # 0, Y₁ and Y₂ are not necessarily dependent. Since Cov(Y₁ Y₂) # 0, we should expect Y₁ and Y₂ to be dependent. O Since Cov(Y₁, Y₂) = 0, we should expect Y₁ and Y₂ to be independent. O Even though Cov(Y₁Y₂) = 0, Y₁ and Y₂ are not necessarily independent.
The density function of X is -120x- 0, f(x) = (2(x - 1), (a) Find the mean E(4X+3); (b) Find the variance 3x+2. 1 < x < 2, elsewhere.
= 10. We do Let X and Y be statistically independent random variables with Var(X) = 4 and Var(Y) not know E[X] or E[Y]. Let Z = 2X +9Y. Calculate the correlation coefficient defined as p(X, Z) = Cov(X,Z) √Var(X)Var(Z)
Q2: (b) Let X₁, X2, X3 be uncorrelated random variables, having the same variance o². Consider the linear transformations Y₁ = X₁ + X₂, X2 + X3. Find the correlations of Y₁, Y; i, Y₂ = X₁ + X3 and Y3 for i + j. =
Let Y be a continuous random variable with √ ½ (2 f(y) = = Find the mean (u) and variance (o²) of Y. (2−y), 0≤ y ≤ 2 elsewhere.
Suppose X is a random variable, whose pdf is defined as follows: 2x = (²x) (u(x) - u(x − 3)) where u(x) is the unit step function. Determine the conditional pdf fx(x 1
3. Let X be a continuous random variable. Let f(x) = c(x − 1)³ and Sx = [1,3]. Hint: (x - 1)³ = x³ + 3x − 3x² - 1 (a) What value of c will make f(x) a valid density? (b) What is P(X = 2)? (c) Find E(X). (d) What is P(1 < X < 2)?
Suppose X and Y are two random variables with E[X] = 1, Var (X) = 4, E[Y ] = -1, Var (Y) 4, and Cov (X, Y) = 1. Find the standard deviation of (X - Y). = (a) 2 (b) √2 (c) 6 (d) √6 (e) None of the above
Prove that the variance of b, V(b) = o²(X'X)−¹

SEE MORE QUESTIONS

Recommended textbooks for you

Algebra & Trigonometry with Analytic Geometry

Algebra

ISBN:

9781133382119

Author:

Swokowski

Publisher:

Cengage

Calculus For The Life Sciences

Calculus

ISBN:

9780321964038

Author:

GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.

Publisher:

Pearson Addison Wesley,

Trigonometry (MindTap Course List)

Trigonometry

ISBN:

9781337278461

Author:

Ron Larson

Publisher:

Cengage Learning

Algebra & Trigonometry with Analytic Geometry

Algebra

ISBN:

9781133382119

Author:

Swokowski

Publisher:

Cengage

Calculus For The Life Sciences

Calculus

ISBN:

9780321964038

Author:

GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.

Publisher:

Pearson Addison Wesley,

Trigonometry (MindTap Course List)

Trigonometry

ISBN:

9781337278461

Author:

Ron Larson

Publisher:

Cengage Learning

SEE MORE TEXTBOOKS