(i) The mean is
The variance is
Compute the second moment :
Then the variance is
(ii) For a random variable , where are constants, we have
and
Then for , we have
Answer:
A and B are not independent events because P(A|B)≠P(A)
is the correct answer.
Step-by-step explanation:
If A and B are independent then we must have
P(AB) = P(A) P(B) and also
P(A/B) = P(A)
We are given that
A and B are two events.
Let P(A)=0.5 , P(B)=0.25 , and P(A and B)=0.15 .
P(A/B) = P(AB)/P(B) = 0.15/0.5 = 0.3
i.e. P(A/B) is not equal P(A)
Similarly P(B/A) = P(AB)/P(A) = 0.15/0.25 = 0.6 not equal to P(B)
Hence A and B are not independent.
The strategy to graph a line actually doesn't depend on the form the equation is presented: it can be the standard form, the slope intercept form, or any other way to write it.
The key point is that you can draw a line if you know two of its points. In fact, all you have to do is draw and connect them.
To sample two points from the equation, just pick any two values for x, and compute the correspondent value for y.
For example, given the line y=3x-7, we can sample x=0 and x=1 (again, this is a totally arbitrary choice), and compute
So, the line passes through the points (0,-7) and (1,-4). Draw these two points and connect them, and you'll have the line.
Answer:
Option C
Step-by-step explanation:
Shaded region of the given graph shows the solution area of inequality with notation of less than (<).
If the basic function in the form of an equation is,
And the graph is shifted 3 units left horizontally,
Equation will be,
Then the solution area of the inequality representing the graph will be,
Option C will be the answer.
Answer:
x = 2
Step-by-step explanation:
Solve for x:
12 - 3 x = 6
Hint: | Isolate terms with x to the left hand side.
Subtract 12 from both sides:
(12 - 12) - 3 x = 6 - 12
Hint: | Look for the difference of two identical terms.
12 - 12 = 0:
-3 x = 6 - 12
Hint: | Evaluate 6 - 12.
6 - 12 = -6:
-3 x = -6
Hint: | Divide both sides by a constant to simplify the equation.
Divide both sides of -3 x = -6 by -3:
(-3 x)/(-3) = (-6)/(-3)
Hint: | Any nonzero number divided by itself is one.
(-3)/(-3) = 1:
x = (-6)/(-3)
Hint: | Reduce (-6)/(-3) to lowest terms. Start by finding the GCD of -6 and -3.
The gcd of -6 and -3 is -3, so (-6)/(-3) = (-3×2)/(-3×1) = (-3)/(-3)×2 = 2:
Answer: x = 2