Question

Let {X_{1}, X_{2}, . . . , X_{36}},
where µ_{X} = 0 and σ^{2}_{X} = 1/36, be a
random sample with mean X(bar) and variance S^{2} . Define
Y = X_{1} + X_{2} + · · · + X_{36}, and
calculate or approximate (indicate which) the following
probabilities:

a. P(Y > 1)

b. P(Y^{2} > 2)

c. P(Y > 3S)

Please give details on answers

Answer #1

a. P(Y > 1)

. P(Y > 1) = P[ Z > ] = 1 - P[ Z < 1 ] = 1 - 0.8413 = 0.1587

**P(Y > 1) = 0.1587**

b. P(Y^{2} > 2) ( square of SNV is chi square )

P(Y^{2} > 2) =
= 0.16

**P(Y ^{2} > 2) = 0.16**

c. P(Y > 3S)

=P[ Z > 3 ]

**P(Y > 3S) = 0.0013**

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