6. Let X be a uniform random variable on the interval [0, b]. Determine b so...

Question

Question

6. Let X be a uniform random variable on the interval [0, b]. Determine b so that σ = 2 √ µ.

math Statistics-And-Probability

Answer 1

Answer #1

For a uniform distribution, = (a + b)/2

=

When = 2 ,

² = 4

4 = (b-a)²/12

= (b-a)²/48

(a+b)/2 = (b-a)²/48

Given that, a = 0

Therefore,

b/2 = b²/48

b = b²/24

1 = b/24

b = 24

Answer 2

Similar Homework Help Questions

Given that X is a continuous random variable that has a uniform probability distribution, and 0...

Given that X is a continuous random variable that has a uniform probability distribution, and 0 < X < 8: a. Calculate P(X < 4) (to 3 significant digits). P(X < 4)= b. Determine the mean (µ) and standard deviation (σ) of the distribution (to 3 significant digits). µ = σ =
.Let X be a uniform random variable on the interval (0, 1). Find the range and...

.Let X be a uniform random variable on the interval (0, 1). Find the range and the distribution and density functions of Y = 3X − 5. Is the variable Y familiar? What is its type?
(20 pts) Let U be a random variable following a uniform distribution on the interval [0...

(20 pts) Let U be a random variable following a uniform distribution on the interval [0 Let X=2U + 1 (a) Is X a random variable? Why or why not? (b) Calculate E[X] analytically

(5 pts) Let U be a random variable following a uniform distribution on the interval [0,...

(5 pts) Let U be a random variable following a uniform distribution on the interval [0, 1]. Let X=2U + 1 Calculate analytically the variance of X. (HINT : Elg(z)- g(z)f(x)dr, and the pdf. 0 < z < 1 0 o.t.w. f(x) of a uniform distribution is f(x) =
Let X be a random variable with E(X) = µ and V (X) = σ 2...

Let X be a random variable with E(X) = µ and V (X) = σ 2 . Let a and b be constants (fixed numbers) and define another random variable Y = aX + b. Find the E[Y ] and V [Y ] in terms of E(X) = µ and V (X) = σ 2 . From your results, tell whether adding or subtracting a constant to the random variable changes its variance.
Problem 1. 15 points] Let X be a uniform random variable in the interval [-1,2]. Let...

Problem 1. 15 points] Let X be a uniform random variable in the interval [-1,2]. Let Y be an exponential random variable with mean 2. Assunne X and Y are independent. a) Find the joint sample space. b) Find the joint PDF for X and Y. c) Are X and Y uncorrelated? Justify your answer. d) Find the probability P1-1/4 < X < 1/2 1 Y < 21 e) Calculate E[X2Y2]

Let X be a uniform random variable over (0,1). Let a and b be two positive...

Let X be a uniform random variable over (0,1). Let a and b be two positive numbers and let Y = aX+b. (a) Determine the moment generating function of X. (b) Determine the moment generating function of Y. (c) Using the moment generating function of Y, show that Y is uniformly distributed over an interval(a, a+b).
Let X be a uniform(0, 1) random variable and let Y be uniform(1,2) with X and...

Let X be a uniform(0, 1) random variable and let Y be uniform(1,2) with X and Y being independent. Let U = X/Y and V = X. (a) Find the joint distribution of U and V . (b) Find the marginal distributions of U.
X is a continuous uniform random variable in interval 0 and 9. A) Calculate E(XA2) of...

X is a continuous uniform random variable in interval 0 and 9. A) Calculate E(XA2) of this random variable. B) Calculate V(X 2)

Let X be a continuous random variable uniformly distributed on the unit interval (0, 1), .e...

Let X be a continuous random variable uniformly distributed on the unit interval (0, 1), .e X has a density f(x) = { 1, 0<r<1 f (x)- 0, elsewhere μ+ơX, where-oo < μ < 00, σ > 0 (a) Find the density of Y (b) Find E(Y) and V(Y)