Suppose that X is a random variable with mean 20 and standard deviation 5. Also suppose that Y is a random variable with mean 40 and standard deviation 10. Assume that the correlation between X and Y is 0.5. Find the mean and variance of the random variable Z = 3X 2Y . Be sure to show all your work.

a

b

c

Step-by-step explanation:

From the question we are told that

   The mean of X  is

   The standard deviation of X is  

   The mean of Y  is

    The standard deviation of Y is  

Considering question a  

Generally the mean of   Z = 2 + 10X. is mathematically  represented

=>

=>          

=>            

Considering question b

Generally the mean of   Z = 10X - 2.. is mathematically  represented  

   =>

  =>  

  =>  

 =>  

Considering question c

Generally the mean of   -3X - 2Y is mathematically  represented

=>  

=>

80π/3 or about 83.775

step-by-step explanation:

since a cone is 1/3 of a cylinder, we need to find the base's area. since area = πr^2, we get 16π. then, multiplying this by 5, we get 80π. dividing by 3, since the cone's volume is 1/3 of that of a cylinder's, we get 80π/3.

hope this !

6/20

step-by-step explanation: