2) (Difficult problem: i don't expect that people can solve it) Let X be a exponential variable with parameter λ 2, Now, we have a unbiased coin. We throw it. If we get tall, we take the number X. If we get head we take 3 times X. The result is called Z. What is the probability density of Z. (Read up about the probability density of exponential variable online). So, in other words, we generate a random number X which is exponential with parameter λ = 2, then, we flip a coin. When we get tail we put Z to be defined by: Z-X, Otherwise when we get head, we define Z-3X. So, Z is half the time equal to exponential with λ 2 and the other half equal to 3 times such an exponential variable. What is probability density function of Z? (HINT: recall that the probability density at the point co is the probability of the variable to be in a small interval around zo devided by the size of that small interval). 2) (Difficult problem: i don't expect that people can solve it) Let X be a exponential variable with parameter λ 2, Now, we have a unbiased coin. We throw it. If we get tall, we take the number X. If we get head we take 3 times X. The result is called Z. What is the probability density of Z. (Read up about the probability density of exponential variable online). So, in other words, we generate a random number X which is exponential with parameter λ = 2, then, we flip a coin. When we get tail we put Z to be defined by: Z-X, Otherwise when we get head, we define Z-3X. So, Z is half the time equal to exponential with λ 2 and the other half equal to 3 times such an exponential variable. What is probability density function of Z? (HINT: recall that the probability density at the point co is the probability of the variable to be in a small interval around zo devided by the size of that small interval).