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# 4. Find the mean and standard deviation of the following probability

### Resolved Question:

4. Find the mean and standard deviation of the following probability distribution:
x 1 2 3
P(x) 0.5 0.3 0.2

Submitted: 5 years ago.
Category: Math Homework
Expert:  David replied 5 years ago.

David :

mean = 1*0.5+2*0.3+3*0.2=1.7
now calculte the expected x^2
1^2*0.5+2^2*0.3+3^2*0.2=3.5
hence the standard deviation is:
stdev = sqrt(3.5-1.7^2)=0.781

David :

Answer: mean = 1.7, standard deviation = 0.781

Customer:

Not understanding the second half of the answer.

David :

ok

David :

to get the standard deviation

David :

you need to calculate the variance first

David :

recall that variance is defined as a difference between the mean of the squares: 1,4,9

David :

and the square of the mean 1.7

David :

the mean of the squares is found to be 3.5

David :

and the variance is hence 3.5-1.7^2 = 0.61

David :

now taking the square root of this we get standard deviation = √0.61 =0.781

David :

is it clear now?

Customer:

I am trying to understand is (1)^2(0.5) or (1)(0.5)^2?

Customer:

I have to show all of my steps

David :

it is one squared times point five

David :

because you need he mean of the squares

David :

the numbers you have are 1,2,3 so the squares are 1, 4, 9

David :

hence 1*0.5+4*0.3+9*0.2=3.5

David :

does it make sense now?

Customer:

yes

David :

OK, good