Question: The question is shown below Exercise 3 (5 + 5 pts.). Sum of mndom variables 1. Let Z N N (0, 1). What is the

The question is shown below

Exercise 3 (5 + 5 pts.). Sum of mndom variables 1. Let Z N N (0, 1). What is the probability density function of X = Z2? 2. Let Z1, Z2, . . . , Zk ~ N(0, 1) be I: independent standard normal random variables. What is the prob- ability density function of Y = Z? + . . . Z3? Hint: Compute I'(1/2) by an adequate change of variables, then recognize the distribution of Z2 computed in the rst

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