8. A random variable has a probability density function given by (4 x - 1 f(x) = 0 ≤ x ≤ 1, ≤ 2, 1 ≤ x otherwise. (This is the same PDF as in the previous question.) A computer simulation will be used in which a sample of the random variable will need to be made. Determine and describe a method to create a way to sample a random variable with the probability density function given above.

Suppose random variable Y represents a random number generator that can take any value between 1 and 11. Then the density curve of the outcomes has constant height between 1 and 11, and height of 0 elsewhere. What’s the height of the density curve between 1 and 11? What is the probability that Y<2? What is the probability that Y=2? Can Y=2 happen as an event for this random number generator? What is the probability that Y=0? Can Y=0 happen as an event for this random number generator?

Please help with this practice problem

Question 1.2 Consider the function  f (x) = (1/24(x^2 +1)      1 < or =  x < or = 4)          = (0      otherwise)   Calculate P (x = 3) Calculate P (2 < or =  x < or = 3)         Question 1.3 Consider the function  f (x) = (k - x/4      1 < or =  x < or = 3)          = (0      otherwise)   which is being used as a probability density function for a continuous random variable x?   a. Find the value of K b. Find P (x < or = 2.5)