MHB -aux.03 P(X-x) find P, find X, from table

[karush]

The probability distribution of the discrete variable X is given by the following table
https://www.physicsforums.com/attachments/1099

(a) Find the value of p where x=2.
(b) Calculate the expected value of X in P(X-x)

I am basically clueless about this, but is $\mu=3$

 

[MarkFL]

a) You want the sum of the probabilities to be 1.

b) $$E[X]=\sum_{k=1}^5x_kP_k$$

What do you find?

 

[karush]

a) You want the sum of the probabilities to be 1.

b) $$E[X]=\sum_{k=1}^5x_kP_k$$

What do you find?

does this mean $p=1-(0.4+0.2+0.07+0.02)=.31$

 

[MarkFL]

does this mean $p=1-(0.4+0.2+0.07+0.02)=.31$

Yes, that's correct.

Now, to find the expect value, find the sum of the products of the x-values and their corresponding probabilities.

 

[karush]

Yes, that's correct.

Now, to find the expect value, find the sum of the products of the x-values and their corresponding probabilities.

$$(1\times0.4)+(2\times.31)+(3\times0.2)+(4\times0.07)+(5\times0.02)=2$$

 

[MarkFL]

$$(1\times0.4)+(2\times.31)+(3\times0.2)+(4\times0.07)+(5\times0.02)=2$$

I get a slightly higher value...are you rounding because $X$ is given as discrete?

 

[karush]

uhmmm, well, don't recall any rounding. just let the WF compute it.

no sure what is meant by discrete

 

[MarkFL]

uhmmm, well, don't recall any rounding. just let the WF compute it.

no sure what is meant by discrete

Did you recompute and get the same value?

As an example, the set of integers is discrete, while the set of real numbers is continuous.

 

[MarkFL]

I get a slightly higher value...are you rounding because $X$ is given as discrete?

I accidentally entered a wrong value in my calculator...2 is correct.

 

[karush]

I accidentally entered a wrong value in my calculator...2 is correct.

no worry, it happens, too often for me even after double checking

just curious what Calc do you have ... I have the TI-Nspire CX CAS.. its really nice
but I go to WF a lot too...

I'll be posting another probability distribution problem next, I seem to be getting the hang of it ... also want to get proficient with box plots

Much Mahalo

 

[MarkFL]

I have a TI-89 Titanium, although in this case I used W|A. Had I used the TI, I might not have made the error as I could have been looking at the data table as I entered the numbers. :D