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 4 decimal places.)

P(X ? ?6)

Solutions

Expert Solution

Given,

Then, the density function f(x) sholud be like

Hence, the height of density function should be

(b) The mean of the distribution is given by

Similarly,

Hence, the standard deviation of the distribution is

(c)

orchestra answered 1 year ago

Next > < Previous

Related Solutions

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) =

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 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...

1) Let x be a continuous random variable that follows a normal distribution with a mean...

1) Let x be a continuous random variable that follows a normal distribution with a mean of 321 and a standard deviation of 41. (a) Find the value of x > 321 so that the area under the normal curve from 321 to x is 0.2224. Round your answer to the nearest integer. The value of x is_______ (b) Find the value of x so that the area under the normal curve to the right of x is 0.3745. Round...

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

Find -A continuous r.v. X follows uniform distribution , that is ? ~ ???????(?=0,?=1), Find the...

Find -A continuous r.v. X follows uniform distribution , that is ? ~ ???????(?=0,?=1), Find the following probability (a) P(0 < X < 0.3) (b) P(0.5 < X < 1) (c) Find the mean and variance of X - A continuous r.v. X follows the pdf: ?(?)= 2?3, 1≤?≤2. (a) Find the cdf of X for 1≤?≤2. (b) Find the mean and variance of X. (c) Find P(X = 1.22) -Suppose that in a particular traffic environment, the distribution of...

Random variable X is a continuous uniform (0,4) random variable and Y=X^(1/2). (Note: Y is always...

Random variable X is a continuous uniform (0,4) random variable and Y=X^(1/2). (Note: Y is always the positive root.) What is the P[X>=E[X]] ? What is the E[Y] ? what is the P[Y>=E[Y]]? what is the PFD of fY(y)?

Let U be a uniform continuous random variable on the interval [2, 8]. (a) What is...

Let U be a uniform continuous random variable on the interval [2, 8]. (a) What is P(U = 4)? (b) What is P(U ≤ 4)? (c) What is P(4 ≤ U ≤ 7)? (d) Find a formula for FU(x). (e) Find a formula for fU(x). (f) What is E(U)? (g) What is Var(U)? (h) What is E(1 − U 2 )?

continuous random variable and uniform distribution please follow the comment. A random number generator spits out...

continuous random variable and uniform distribution please follow the comment. A random number generator spits out a random real number in the range [1,4] assume each number is equally likely being out. what is the probability that the model output an irrational number? the answer is 1, but i don't understand

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.

Subjects