The third one is the correct graph for the equation
hope it helps !!
Answer and Explanation:
Given : The random variable x has the following probability distribution.
To find :
a. Is this probability distribution valid? Explain and list the requirements for a valid probability distribution.
b. Calculate the expected value of x.
c. Calculate the variance of x.
d. Calculate the standard deviation of x.
Solution :
First we create the table as per requirements,
x P(x) xP(x) x² x²P(x)
0 0.25 0 0 0
1 0.20 0.20 1 0.20
2 0.15 0.3 4 0.6
3 0.30 0.9 9 2.7
4 0.10 0.4 16 1.6
∑P(x)=1 ∑xP(x)=1.8 ∑x²P(x)=5.1
a) To determine that table shows a probability distribution we add up all five probabilities if the sum is 1 then it is a valid distribution.


Yes it is a probability distribution.
b) The expected value of x is defined as

c) The variance of x is defined as

d) The standard deviation of x is defined as



Answer:
-5
Step-by-step explanation:
8y-6y=-3-7
2y=-10
y=-10÷2
y=-5
-4(x + 1) + 5 = 17
Distribute -4 inside the parentheses.
(-4x - 4) + 5 = 17
Combine like terms (-4 + 5).
-4x + 1 = 17
Subtract 1 from both sides.
-4x = 16
Divide both sides by -4.
x = -4
-60 -49 -40 9
-45 -18 80 82
-74 -23 14 85
-79 -68 21 46
-48 -21 27 54
-68 -13 4 32