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

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The discussion revolves around calculating the probability and expected value for a discrete variable X based on a provided probability distribution table. Participants confirm that the value of p when x=2 is 0.31, ensuring the sum of probabilities equals 1. The expected value E[X] is calculated using the formula E[X]=Σx_kP_k, resulting in a value of 2 after verifying calculations. There is a brief exchange about the importance of accuracy in calculations, particularly when using different calculators. The conversation concludes with a mention of future probability distribution problems and a desire to improve skills in box plots.
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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 $\mu=3$
 
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a) You want the sum of the probabilities to be 1.

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

What do you find?
 
MarkFL said:
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 $p=1-(0.4+0.2+0.07+0.02)=.31$
 
karush said:
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.
 
MarkFL said:
Yes, that's correct.

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

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

I get a slightly higher value...are you rounding because $X$ is given as discrete?
 
uhmmm, well, don't recall any rounding. just let the WF compute it.

no sure what is meant by discrete
 
karush said:
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 said:
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.
 
  • #10
MarkFL said:
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
 
  • #11
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
 

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