Consider a random variable X that is Gaussian distributed with mean 33 and variance 17. In this problem, you will consider a scenario where additional conditions are placed on X to define a new random variable. (a) Write the probability density function (pdf) for X. (b) Find the probability: P(0 x 20). (c) Find the probability that X is positive (X 20). (d) Find the conditional pdf fx(r[X 20) (e) Find the conditional probability: P(X 201X 20). 2. Consider a Gaussian random variable X with mean -5 and standard deviation 14. A random variable Y is related to X by the equation given. Use this information to answer the questions below. Y-12X +90 (a) Find the probability that X -10. (e) Find the probability that -20 < X < 10 (d) Find the probability that Y < 45. (e) Find the probability that Y> 60. (f) Find the probability that 0