If a random variable has a uniform distribution over the range 10 ≤X≤ 20, what is...

If a random variable has a uniform distribution over the range 10 ≤X≤ 20, what is the probability that the random variable takes a value in the range [13.75, 17.25]?

Expert Solution

X ~ U (10 , 20)

P(13.75 < X < 17.25) = (17.25 - 13.75) / (20 - 10) = 0.35 (ans)

milcah answered 10 months 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

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...

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.

The random variable X follows a CONTINUOUS UNIFORM DISTRIBUTION over the interval [50, 250]. Find P(80...

The random variable X follows a CONTINUOUS UNIFORM DISTRIBUTION over the interval [50, 250]. Find P(80 < X < 135). P(80 < X < 135) =

A random variable X follows the continuous uniform distribution with a lower bound of ?8 and...

A random variable X follows the continuous uniform distribution with a lower bound of ?8 and an upper bound of 11. a. What is the height of the density function f(x)? (Round your answer to 4 decimal places.) f(x) b. What are the mean and the standard deviation for the distribution? (Round your answers to 2 decimal places.) Mean Standard deviation c. Calculate P(X ? ?6). (Round intermediate calculations to 4 decimal places and final answer to...

1) A discrete random variable X has the following probability distribution: x 13 18 20 24...

1) A discrete random variable X has the following probability distribution: x 13 18 20 24 27 p(x) 0.22 0.25 0.2 0.17 0.16 Compute each of the following quantities (give the exact numbers): (a) P(18)= (b) P(X>18)= (c) P(X?18)= (d) The mean ? of X is (e) The variance ?2 of X is (write all decimal points) (f) The standard deviation ? of X is (use 4 decimal points) 2) Borachio works in an automotive tire factory. The number X...

1. Suppose x is a random variable best described by a uniform probability distribution with and Find 2....

1. Suppose x is a random variable best described by a uniform probability distribution with and Find 2. Suppose x is a random variable best described by a uniform probability distribution with and Find 3. Suppose x is a random variable best described by a uniform probability distribution with and Find 4. Suppose x is a random variable best described by a uniform probability distribution with and Find 5. Suppose x is a random variable best described by a uniform probability distribution with and Find 6. Suppose x is a...

The random variable X follows a normal distribution with a mean of 10 and a standard...

The random variable X follows a normal distribution with a mean of 10 and a standard deviation of 3. 1. What is P(7≤X≤13)? Include 4 decimal places in your answer. 2. What is the value of k such that P(X>k)=0.43? Include 2 decimal places in your answer.

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 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).

Question