Computing principles

5 Random variables X and yare independent random variables. The random variable x has chi- square distribution with 1 degree of freedom . The sum of random variables Xty has a chi- square distribution with 3 degrees of freedom. a,) The random variable yhas a distribution. I, normal II. Chebychev's V. F IL. binomial II. chi-square II. Not enough inform. b. The random variable yhas degrees of freedom I. D II. 2 V.4 I.1 IV.3 VI Not enough information3.3.1 Counting principles Knewton Alta MATH 1340 C1608 2020WI - STATISTICS 3.3.1 Counting principles Counting with combinations Question A manager is scheduling 24 employees for different shifts. If he needs to choose 8 employees for each shift, how many different groups of eight employees can he make without repetition? Provide your answer below:Prob. 5 Let X be an exponentially distributed random variable with probability density function (PDF) given by Sie-2 fx (x) = 10, x 2 0 otherwise Consider the random variable Y = VX . (a) Determine the hazard rate function for the random variable Y. (b) Give an algorithm for generating the random variable Y from a standard uniform random variable U. (c) Choose a value for the parameter 1 so that the variance of the random variable Y is twice its mean.a. Let X be a random variable with PDF given by: fx(x) = 3\"\