Define random variable X ~ Uniform(0, 8). a) What is the probability density function f(X)?

Buses depart from a bus stop every 10 minutes from 00:00. One person came to the bus stop without knowing the timetable. Let's say he will take the bus. The random variable X denotes the time this person has to wait. Find R_X and f_X. (R_X denotes the image of X and f_X denotes the probability mass/density function of X)

Let X be a uniform random variable on the interval (-3,3) and let Y = X^2 A) find E(Y). B) find the probability density function of Y

The random-number generator on calculators randomly generates a number between 0 and 1. The random variable X, the number generated, follows a uniform probability distribution. (a) Identify the graph of the uniform density function. (b) What is the probability of generating a number between 0.37 and 0.69? (c) What is the probability of generating a number greater than 0.83? ... OA. В. OC. Density 1.2- A Density 1.2- ADensity 1.2- 1- 1. 1- 0.8- 0.8- 0.6- 0.4- 0.2- 0+ 0.8- 0.6- 0.6- 0.4- 0.2- 04 0 0.2 0.4 0.6 0.8 1 0.4- 0.2- X 0- 0.2 0.4 0.6 0.8 1 1.2 1.2 0.2 0.4 0.6 0.8 1 1.2 (b) The probability is (Simplify your answer.) (c) The probability is (Simplify your answer.) B.