Let X be a continuous random variable such that E[Xm] exists where m is some positive...

Let X be a continuous random variable such that E[X^m] exists where m is some positive integer. Prove that if k is a positive integer and k < m, then E[X^k] exists.

Solutions

Expert Solution

orchestra answered 1 year ago

Next > < Previous

Related Solutions

Does a continuous random variable X exist with E(X − a) = 0, where a is...

Does a continuous random variable X exist with E(X − a) = 0, where a is the day of your birthdate? If yes, give an example for its probability density function. If no, give an explanation. (b) Does a continuous random variable Y exist with E (Y − b) 2 = 0, where b is the month of your birthdate? If yes, give an example for its probability density function. If no, give an explanation.

(a) Let X be a continuous random variable which only takes on positive values on the...

(a) Let X be a continuous random variable which only takes on positive values on the interval [1, 4]. If P(X) = (√ x + √ 1 x )C 2 for all x in this interval, compute the value of C. (b) Let X be a random variable with normal distribution. Let z represent the z-score for X, and let a be a positive number. Prove that P(z < |a|) = P(z < a) + P(z > −a) − 1.

Let X be a random variable with CDF F(x) = e-e(µ-x)/β, where β > 0 and...

Let X be a random variable with CDF F(x) = e-e(µ-x)/β, where β > 0 and -∞ < µ, x < ∞. 1. What is the median of X? 2. Obtain the PDF of X. Use R to plot, in the range -10<x<30, the pdf for µ = 2, β = 5. 3. Draw a random sample of size 1000 from f(x) for µ = 2, β = 5 and draw a histogram of the values in the random sample...

Let X and Y be continuous random variables with E[X] = E[Y] = 4 and var(X)...

Let X and Y be continuous random variables with E[X] = E[Y] = 4 and var(X) = var(Y) = 10. A new random variable is defined as: W = X+2Y+2. a. Find E[W] and var[W] if X and Y are independent. b. Find E[W] and var[W] if E[XY] = 20. c. If we find that E[XY] = E[X]E[Y], what do we know about the relationship between the random variables X and Y?

1. Let X be a continuous random variable such that when x = 10, z =...

1. Let X be a continuous random variable such that when x = 10, z = 0.5. This z-score tells us that x = 10 is less than the mean of X. Select one: True False 2. If an economist wants to determine if there is evidence that the average household income in a community is different from $ 32,000, then a two-tailed hypothesis test should be used. Select one: True False 3. α (alpha) refers to the proportion of...

Let x be a continuous random variable that follows a distribution skewed to the left with...

Let x be a continuous random variable that follows a distribution skewed to the left with ?= 92 and ?=15. Assuming n/N <= .05, find the probability that the sample mean, x bar, for a random sample of 62 taken from this population will be (ROUND ANSWERS TO FOUR DECIMAL PLACES): a) less than 81.5 P(less that 81.5)= b) greater than 89.7 P(greater than 89.7)= Please show your work.

Let x be a continuous random variable that is normally distributed with a mean of 65...

Let x be a continuous random variable that is normally distributed with a mean of 65 and a standard deviation of 15. Find the probability that x assumes a value: less than 48 greater than 87 between 56 and 70

Let X be a continuous random variable with a probability density function fX (x) = 2xI...

Let X be a continuous random variable with a probability density function fX (x) = 2xI (0,1) (x) and let it be the function´ Y (x) = e −x a. Find the expression for the probability density function fY (y). b. Find the domain of the probability density function fY (y).

2] Let x be a continuous random variable that has a normal distribution with μ =...

2] Let x be a continuous random variable that has a normal distribution with μ = 48 and σ = 8 . Assuming n N ≤ 0.05 , find the probability that the sample mean, x ¯ , for a random sample of 16 taken from this population will be between 49.64 and 52.60 . Round your answer to four decimal places.

Let x be a continuous random variable that has a normal distribution with μ = 60...

Let x be a continuous random variable that has a normal distribution with μ = 60 and σ = 12. Assuming n ≤ 0.05N, where n = sample size and N = population size, find the probability that the sample mean, x¯, for a random sample of 24 taken from this population will be between 54.91 and 61.79. Let x be a continuous random variable that has a normal distribution with μ = 60 and σ = 12. Assuming n...

Subjects