The repair time (in hours) for a certain machine is a random variable with probability density function (xe S(x) = What is the probability that the repair time is less than 2 hours? b. a. What is the probability that the repair time is between 1.5 and 3 hours? Find the mean repair time. d. C. Find the cumulative distribution function of the repair times.

Let x be a continuous random variable that is normally distributed with a mean of 22 and a standard deviation of 5. Find to 4 decimal places the probability that x assumes a value a. between 26 and 34. Probability = i b. between 18 and 31. Probability i

The table below represents the probability density function for the random variable X. Find the standard deviation of X. Round the final answer to two decimal places. x   P(X = x)  1  1/4  3  1/4  4  1/2

Q1. Suppose X is a continuous random variable. Find an example of a probability density function for X giving expected value E(X) = 1 and variance V (X) = 3 if X has . . .  (a.) a uniform distribution. (b.) an exponential distribution. (c.) a normal distribution. In each case, if there is no such probability density function, explain why this is so.

3. The level of impurity (in percent) in the product of a certain chemical process is a random variable with probability density function 3 64 -x²(4 - x) 0 0 < x < 4 otherwise a. What is the probability that the impurity level is greater than 3%? b. What is the probability that the impurity level is between 2% and 3%? c. Find the mean impurity level. d. Find the variance of the impurity levels.

1 Given the probability density function f(x) = over the interval [3,6], find the expected value, the mean, 3 the variance and the standard deviation. Expected value: Mean: Variance: Standard Deviation: > Next Question

he chance of an IRS audit for a tax return with over $25,000 in income is about 2% per year. We are interested in the expected number of audits a person with that income has in a 10-year period. Assume each year is independent. Give the distribution of X.X ~

Assume that the coin is flipped 4 times, and the random variable X is defined to be 2 times the number of heads minus 4 times the number of tails. How many different values are posslbe for the random variable X? Answer: 5 Fill in the table below to complete the probability density function. Be certain to list the values of X in ascending order Values of X (these are all correct. I need help with finding the probabilities) -16, -10, -4, 2, 8 What are the probabilities? Thanks!