I need help with question 5.22, the picture attached, please!

5.21 What is the probability that the larger of two continuous iid random variables will exceed the population median? Generalize this result to samples of size n. do I Te. 5.22 Let X and Y be iid n(0, 1) random variables, and define Z = min(X, Y). Prove that z? ~ x?- 5.23 Let Ui, i = 1, 2, ..., be independent uniform(0, 1) random variables, and let X have distribution colqurexa of' bealleb ate A bus y bredw AV to 1bq odds buis (d bis (it) X (no)X Jol bus P(X =x) = x= 1, 2,3, . .., i, ed me ibg onia lo anrot fl .ealjaitsde isbio lo aquora intojeth owt yna sd (moX > > Gith where c = 1/(e - 1). Find the distribution of x baa (@), ibo 9/) bus (x)xt Z = min{Ui, . . ., Ux }.as 1bo lanigzem onT (s) A to the bus lbo lenolibnoo edT (d) (Hint: Note that the distribution of Z X = x is that of the first-order statistic from 00! to saxod hi many eegsxosq aisblood to 191019010 UX.0 a sample of size x.) with pdf gil1 93879V8