Question

Let Y be the liner combination of the independent random variables X1 and X2 where Y...

Let Y be the liner combination of the independent random variables X1 and X2 where Y = X1 -2X2

suppose X1 is normally distributed with mean 1 and standard devation 2

also suppose the X2 is normally distributed with mean 0 also standard devation 1

find P(Y>=1) ?

Math   Statistics-And-Probability   
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Answer #1

X1 is normally distributed with mean 1 and standard deviation 2

X2 is normally distributed with mean 0 also standard deviation 1

Therefore 2X2 is normally distributed with mean = 2*0 =0 also standard deviation =2*1 = 2

Given Y = X1 -2X2

Therefore Y is normally distributed with mean µ = 1 - 0 = 1 also standard deviation σ = = 2.8284

P( Y ≥ 1 )

=

= P( z ≥ 0 )

= 1 - P( z ≤ 0 )

= 1 - 0.5 ---- ( 0.5 is table value for 0 , using z score table )

P( Y ≥ 1 ) = 0.5

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