A random number generator is used to generate a real number between 0 and 1, equally likely to fall anywhere in this interval of values. (For instance, 0.3794259832c is a possible outcome.)
a. Sketch a curve of the probability distribution of this random variable, which is the continuous version of the uniform distribution (see Exercise 6.1).
b. The probability that the number falls in the interval from 0 to the mean is 50%. Find the mean. (Remember that the total area under the probability curve is 1.)
c. Find the probability that the random number falls between 0.35 and 0.75.
d. Find the probability that the random number is less than 0.8?