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1 answer:
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Y - 10 =(-1/3) ( X - 10 )
Y = ( -1/3) X + ( 40/3)
Step-by-step explanation:
Step 1:
The basic form of Slope Intercept equation is
Step 2:
Points are (10,10) and m=-1/3
Y-10 = (-1/3)(X-10)
Y = ( (-X + 10 )/3) + 10
Y =( - X / 3 ) +( 40 / 3)
The result for the given normal random variables are as follows;
a. E(3X + 2Y) = 18
b. V(3X + 2Y) = 77
c. P(3X + 2Y < 18) = 0.5
d. P(3X + 2Y < 28) = 0.8729
<h3>What is normal random variables?</h3>Any normally distributed random variable having mean = 0 and standard deviation = 1 is referred to as a standard normal random variable. The letter Z will always be used to represent it.
Now, according to the question;
The given normal random variables are;
E(X) = 2, V(X) = 5, E(Y) = 6, and V(Y) = 8.
Part a.
Consider E(3X + 2Y)
Part b.
Consider V(3X + 2Y)
Part c.
Consider P(3X + 2Y < 18)
A normal random variable is also linear combination of two independent normal random variables.
Thus,
Part d.
Consider P(3X + 2Y < 28)
Therefore, the values for the given normal random variables are found.
To know more about the normal random variables, here
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The correct question is-
X and Y are independent, normal random variables with E(X) = 2, V(X) = 5, E(Y) = 6, and V(Y) = 8. Determine the following:
a. E(3X + 2Y)
b. V(3X + 2Y)
c. P(3X + 2Y < 18)
d. P(3X + 2Y < 28)