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:
V = pi * R^2 * h
R = (V / (pi * h))^1/2 = (141.3 / (3.14 * 5))^1/2 = 3 cm
I'm so confused what do you need help with?
Answer:
The number that was added to the previous number is doubled.
For example:
2+1 = 3
2x1= 2
3+2= 5
2x2=4
5+4=9
4x2=8
8+9=17
I hope this helps:)
The general equation of the sine function y=f(x) is defined as

where A is the Amplitude
B represents the frequency of the function with period equals 
C represents the Horizontal shift, For Phase shift= -C/B
D represents the Vertical shift.
The data given that the amplitude of the function A=6

Vertical shift 
Horizontal Shift 
Now plug in
in the general equation of sine function, we get
