3 Let X be a continuous random variable with PDF fxx equal t

3.

Let X be a continuous random variable with PDF fx(x) equal to:

Fx(x)={(k/6)x, 0<=x<=4 and 0 otherwise

A) find the value of the multiplicative constant k such that fx(x) is a legitimate PDF.

B) find the mean(expected value) of X.

C) Find the median of X.

PLEASE SHOW STEPS!

4. [20pts] In a Mexican restaurant, a waitress notices that 45% of the customers order a burrito and 60% of the customers order a soda. Define the events: A A - [a randomly selected customer orders a burrito a randomly selected customer orders a burrito B a randomly selected customer orders a soda) Suppose we know that 30% of the customers order both a burrito and a soda. (a) [Spts] What is the probability that a customer orders either a burrito or a soda or both? (b) [10pts] Are events A and B independent? Justify your ans wer. (c) [5pts] What is the probability that a customer orders a soda given that they order a burrito?

Solution