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(a) Let Z be a standard normal random variable and let U be a random variable distributed as n2, where Z and U are independent. (i) Name the distribution of T=U/nZ and state the value(s) of its parameter(s). (ii) Name the distribution of T2 and state the value(s) of its parameter(s). Justify your answer. (b) Let Y be a random variable distributed as F1,5. (i) Use your answer to part (a), together with the statistical tables for the t distribution (note: NOT the tables for the F distribution), to find P(Y>9). (ii) Use the table for the percentage points of the t distribution to find the median of Y (recall the definition of the median of a random variable given in Chapter 3 of the lecture notes and handouts)..

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(a) Let Z be a standard normal random variable and let U be a random variable distributed as n2, where Z and U are independent. (i) Name the distribution of T=U/nZ and state the value(s) of its parameter(s). (ii) Name the distribution of T2 and state the value(s) of its parameter(s). Justify your answer. (b) Let Y be a random variable distributed as F1,5. (i) Use your answer to part (a), together with the statistical tables for the t distribution (note: NOT the tables for the F distribution), to find P(Y>9). (ii) Use the table for the percentage points of the t distribution to find the median of Y (recall the definition of the median of a random variable given in Chapter 3 of the lecture notes and handouts).

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a Let Z be a standard normal random variable and let U be .pdf

  • 1. (a) Let Z be a standard normal random variable and let U be a random variable distributed as n2, where Z and U are independent. (i) Name the distribution of T=U/nZ and state the value(s) of its parameter(s). (ii) Name the distribution of T2 and state the value(s) of its parameter(s). Justify your answer. (b) Let Y be a random variable distributed as F1,5. (i) Use your answer to part (a), together with the statistical tables for the t distribution (note: NOT the tables for the F distribution), to find P(Y>9). (ii) Use the table for the percentage points of the t distribution to find the median of Y (recall the definition of the median of a random variable given in Chapter 3 of the lecture notes and handouts).