(4) Let X be a discrete random variable with domain D. Prove thatVar(X) = E(X?) – E(X).

Answered: Image /qna-images/answer/f05dc675-fc2a-4a7f-8019-e517d03b1879.jpg

Answered: (4) Let X be a discrete random variable…

Algebra & Trigonometry with Analytic Geometry

13th Edition

ISBN:9781133382119

Author:Swokowski

Publisher:Swokowski

Chapter10: Sequences, Series, And Probability

Section10.8: Probability

Problem 31E

See similar textbooks

Similar questions

Repeat Example 5 when microphone A receives the sound 4 seconds before microphone B.
Show that for any random variable E[X2]≥ (E[X])² and When does one have equality?
Let X and Y be independent random variables, prove that Var (XY) = Var (X) Var (Y) if E [X] = E[ Y] = 0.
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).
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
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
Let X be a random variable such that E(X²) a. V(3X-3) b. E(3x-3) = 58 and V(X) = 40. Compute
X is a continuous random variable having p.d.f. f(x) such that f(x) = kr Osx55 otherwise Find : (a) the constant k; (b) P(15XS 2); (c) (d (e) (f) E(X); E(3X + 1); E(X?); Var (X); (g) Var (4X - 5);
(ii) Suppose that X₁ and X₂ have joint pdf 2, 10, Compute the joint pdf of random variables Y₁ = X₁ and Y₂ = X2. f(x1, x₂): for 0 < x1 < x₂ < 1 otherwise =
4. Assume that X is an exponential random variable. Suppose further that Var(X) = 5. E(X). (a) Find the parameter 0> 0. (b) Compute Var(X + 4). (c) Compute P(X > 15[X > 11).
Let X U(4) find Var(3x) and distribution function.
Q1 Let X be a non-negative discrete random variable. Prove that the expected value of X satisfies E(X) = √ ** (1 – F(x)) da -

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

(4) Let X be a discrete random variable with domain D. Prove that Var(X) = E(X?) – E(X).