Question

Let {X1, X2, . . . , X36}, where µX = 0 and σ2X = 1/36,...

Let {X1, X2, . . . , X36}, where µX = 0 and σ2X = 1/36, be a random sample with mean X(bar) and variance S2 . Define Y = X1 + X2 + · · · + X36, and calculate or approximate (indicate which) the following probabilities:

a. P(Y > 1)

b. P(Y2 > 2)

c. P(Y > 3S)

Please give details on answers

Math   Statistics-And-Probability   
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Homework 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(Y2 > 2) ( square of SNV is chi square )

P(Y2 > 2) = = 0.16

P(Y2 > 2) = 0.16

c. P(Y > 3S)

=P[ Z > 3 ]

P(Y > 3S) = 0.0013

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