Line segment PQ, with endpoints graphed on a coordinate grid at P(2,-2) and Q(5,-2) is translated four units to the left and two
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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)
The parent function passes through the point
, since
Your function passes through the point , which means that the parent function has been translated 3 units up.
To translate a function vertically, you have to add a constant, i.e. you have to transform
k is the amount of units you want to translate: positive if you translate upwards, negative if you translate downwards.
In your case, you move 3 units upwards, so you want k=3 and your function is