(a) If X is a uniform random variable with positive probability on the interval [0, n],...

(a) If X is a uniform random variable with positive probability on the interval [0, n], find the probability density function of e^X

(b) If X is a uniform random variable with positive probability on the interval [1, n], find E [1/X].

Expert Solution

orchestra answered 1 year ago

A random variable X follows a uniform distribution on the interval from 0 to 20. This...

A random variable X follows a uniform distribution on the interval from 0 to 20. This distribution has a mean of 10 and a standard deviation of 5.27. We take a random sample of 50 individuals from this distribution. What is the approximate probability that the sample mean is less than 9.5

Suppose X is a uniform random variable on the interval (0, 1). Find the range and...

Suppose X is a uniform random variable on the interval (0, 1). Find the range and the distribution and density functions of Y = Xn for n ≥ 2.

2. Let X be a uniform random variable over the interval (0, 1). Let Y =...

2. Let X be a uniform random variable over the interval (0, 1). Let Y = X(1-X). a. Derive the pdf for Y . b. Check the pdf you found in (a) is a pdf. c. Use the pdf you found in (a) to find the mean of Y . d. Compute the mean of Y by using the distribution for X. e. Use the pdf of Y to evaluate P(|x-1/2|<1/8). You cannot use the pdf for X. f. Use...

X is uniform in the interval (0, Y ), but Y is itself random, and has...

X is uniform in the interval (0, Y ), but Y is itself random, and has uniform distribution in interval (0, 0.1). What is the probability that X > 0.07? I believe we have to use conditional probability. Please show all steps.

X is an independent standard uniform random variable X ∼ Uniform(0, 1) Y is an independent...

X is an independent standard uniform random variable X ∼ Uniform(0, 1) Y is an independent standard uniform random variable Y ∼ Uniform(0, 1) U = min(X, Y ) V = max(X, Y ) Find the correlation coefficient of V and U , ρ(U, V) = Correlation(U, V).

Let U be a continuous uniform variable over the interval [0, 1]. What is the probability...

Let U be a continuous uniform variable over the interval [0, 1]. What is the probability that U falls within kσ of its mean for k = 1, 2, 3?

Let X be a uniform random variable with pdf f(x) = λe−λx for x > 0,...

Let X be a uniform random variable with pdf f(x) = λe−λx for x > 0, and cumulative distribution function F(x). (a) Show that F(x) = 1−e −λx for x > 0, and show that this function satisfies the requirements of a cdf (state what these are, and show that they are met). [4 marks] (b) Draw f(x) and F(x) in separate graphs. Define, and identify F(x) in the graph of f(x), and vice versa. [Hint: write the mathematical relationships,...

The probability distribution of a discrete random variable x is shown below. X 0 &

The probability distribution of a discrete random variable x is shown below. X 0 1 2 3 P(X) 0.25 0.40 0.20 0.15 What is the standard deviation of x? a. 0.9875 b. 3.0000 c. 0.5623 d. 0.9937 e. 0.6000 Each of the following are characteristics of the sampling distribution of the mean except: a. The standard deviation of the sampling distribution of the mean is referred to as the standard error. b. If the original population is not normally distributed, the sampling distribution of the mean will also...

Let X be a continuous random variable that has a uniform distribution between 0 and 2...

Let X be a continuous random variable that has a uniform distribution between 0 and 2 and let the cumulative distribution function F(x) = 0.5x if x is between 0 and 2 and let F(x) = 0 if x is not between 0 and 2. Compute 1. the probability that X is between 1.4 and 1.8 2. the probability that X is less than 1.2 3. the probability that X is more than 0.8 4. the expected value of X...

Let X and Y be random variable follow uniform U[0, 1]. Let Z = X to...

Let X and Y be random variable follow uniform U[0, 1]. Let Z = X to the power of Y. What is the distribution of Z?

Question