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Vilka [71]
3 years ago
10

Simplify these expressions a) 5 x x b) 6 xxxy c) 2 xxx 3xy

Mathematics
1 answer:
Gennadij [26K]3 years ago
4 0
5x^2
6x^3y
2x^3 3xy
^ means the little number above x eg x^3
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1 year ago
and are independent Gaussian (Normal) random Variables. has mean 13.9 and variance 5.2; has mean 6.9 and variance 3.8. . (a) Cal
omeli [17]

This question is incomplete, the complete question is;

X and Y are independent Gaussian (Normal) random Variables. X has mean 13.9 and variance 5.2; Y has mean 6.9 and variance 3.8. . (a) Calculate P( W> 10)

Answer:

P( W> 10) is 0.1587

Step-by-step explanation:

Given that;

X ⇒ N( 13.9, 5.2 )

Y ⇒ N( 6.9, 3.8 )

W = X - Y

Therefore

E(W) = E(X) - E(Y)

= 13.9 - 6.9 = 7

Var(W) = Var(X) + Var(Y) -2COV(X.Y)

[ COV(X,Y) = 0 because they are independent]

Var(W) = 5.2 + 3.8 + 0

= 9

Therefore

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so

P( W > 10 )

= 1 - P( W ≤ 10 )

= 1 - P( W-7 /3   ≤   10-7 /3 )

= 1 - P( Z ≤ 1 )           [ Z = W-7 / 3 ⇒ N(0, 1)  ]

from Standard normal distribution table, P( Z ≤ 1 )  = 0.8413

so

1 - P( Z ≤ 1 )  = 1 - 0.8413 = 0.1587

Therefore P( W> 10) is 0.1587

8 0
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