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

Solutions

Expert Solution

Probability of model output an irrational number is 1 because random number generator generally generates values upto 6 to 10 decimal places which is an irrational number. Therefore, every real number generated by random number generator in the range [1,4] is an irrational number.

To generate random number we need a calculator or mathematical software. I am using R studio to generate random number from uniform distribution [1,4]. Look at the image below:

I have generated 10 random number first and then 100 random number from uniform distribution[1,4]. In both cases all random numbers generated are irrational number i.e real number in 6 decimals.

Probability laws states that probability ranges from 0 to 1.

Probability is equal to 1 means that event is certain to happen which is in the case of above question. Irrational number is generated everytime, therefore, it is certain to happen. Therefore, probability is 1.

orchestra answered 1 year ago

Next > < Previous

Related Solutions

A random number generator returns random floats between 0 and 1, according to a uniform distribution....

A random number generator returns random floats between 0 and 1, according to a uniform distribution. say you let the random number generator draw 100 numbers, the sample mean will be... A.impossible to determine, because the data aren't drawn from a normal distribution. B.normally distributed, with mean 0.5 and standard deviation 0.2887. C.uniformely distributed, between 0 and 1. D.normally distributed, with mean 0.5 and standard deviation 0.02887.

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...

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...

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 number generator picks a number from 7 to 68 in a uniform manner. Round...

A random number generator picks a number from 7 to 68 in a uniform manner. Round answers to 4 decimal places when possible. The mean of this distribution is The standard deviation is The probability that the number will be exactly 42 is P(x = 42) = The probability that the number will be between 16 and 28 is P(16 < x < 28) = The probability that the number will be larger than 48 is P(x > 48) =...

A random number generator picks a number from 18 to 64 in a uniform manner. Round...

A random number generator picks a number from 18 to 64 in a uniform manner. Round answers to 4 decimal places when possible. The mean of the distribution is: The standard deviation is: The probability that the number will be exactly 20 is P(x = 20) = The probability that the number will be between 24 and 26 is P(24 < x < 26) = The probability that the number will be larger than 32 is P(x > 32) =...

Suppose you have access to a random number generator Rng() that generates uniform random numbers in...

Suppose you have access to a random number generator Rng() that generates uniform random numbers in {0, 1, . . . , n − 1}. Design a function uses Rng() generate a uniform random number in {0, 1, . . . , m − 1}, where m ≤ n

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 )?

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 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.

Subjects