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
W ⇒ N( 7, 9 )
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
You would use this formula for the problem...
(C=2πr) The circumference equals 2 multiplied by pi and radius.
In this problem it says diameter, but the diameter is just twice the length of the radius, so just multiply the radius by 2. Plugin your number.
C=2π(2) since 2 is half of 4, that's your radius.
Your answer is roughly C= 12.57.
You're welcome.
Answer:
2x + 1 
Step-by-step explanation:
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Answer:
27
Step-by-step explanation:
Answer:
30 Lower level tickets
17 upper level tickets
Step-by-step explanation:
Let:
Lower level tickets = l
Upper level tickets = u
5l + 9u = 303 - - - (1)
8l + 10u = 410 - - - - - (2)
Multiply (1) by 8 and (2) by 5
40l + 72u = 2424 - - - (3)
40l + 50u = 2050 - - - (4)
Subtract (3) from (4)
22u = 374
u = 374 / 22
u = 17
Put u = 17 in (1)
40l + 72(17) = 2424
40l + 1224 = 2424
40l = 2424 - 1224
40l = 1200
l = 1200 / 40
l = 30
30 Lower level tickets
17 upper level tickets
