[Steps Shown] Consider independent random variables Zi ~ N(0,1), i=1,….., 16, and let Z̄ be the sample mean. Find: P [ Z̄ < ½] P [Z 1 -Z 2 < 2] P [Z 1 +
Question: Consider independent random variables Zi ~ N(0,1), i=1,….., 16, and let \(\bar{Z}\) be the sample mean. Find:
- P [ \(\bar{Z}\) < ½]
- P [Z 1 -Z 2 < 2]
- P [Z 1 + Z 2 < 2]
- P [ \(\sum\limits_{i=1}^{16}{Z_{i}^{2}}<32\) ]
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P [ \(\sum\limits_{i=1}^{16}{{{\left( {{Z}_{i}}-\bar{Z} \right)}^{2}}}<25\) ].
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