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

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In summary, The discrete variable X has a probability distribution given by the table provided. To find the value of p where x=2, the sum of the probabilities should be 1. The expected value of X can be calculated using the formula E[X]=\sum_{k=1}^5x_kP_k, where x_k is the x-value and P_k is its corresponding probability. In this case, the expected value is 2. The set of integers is an example of a discrete set, while the set of real numbers is continuous.
  • #1
karush
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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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  • #2
a) You want the sum of the probabilities to be 1.

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

What do you find?
 
  • #3
MarkFL said:
a) You want the sum of the probabilities to be 1.

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

What do you find?

does this mean $p=1-(0.4+0.2+0.07+0.02)=.31$
 
  • #4
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.
 
  • #5
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.

\(\displaystyle (1\times0.4)+(2\times.31)+(3\times0.2)+(4\times0.07)+(5\times0.02)=2\)
 
  • #6
karush said:
\(\displaystyle (1\times0.4)+(2\times.31)+(3\times0.2)+(4\times0.07)+(5\times0.02)=2\)

I get a slightly higher value...are you rounding because $X$ is given as discrete?
 
  • #7
uhmmm, well, don't recall any rounding. just let the WF compute it.

no sure what is meant by discrete
 
  • #8
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.
 
  • #9
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
 

1. What does "-aux.03 P(X-x) find P" mean?

This expression is a notation used in probability and statistics. The "-aux.03" indicates that the probability distribution is continuous, while P(X-x) indicates the probability of an event occurring within a specific range of values for a continuous variable X. The "find P" part means that you are being asked to calculate the probability of the event occurring within that range.

2. How do I find the value of P in "-aux.03 P(X-x) find P"?

To find the value of P, you will need to use a probability distribution table or a statistical software program. First, identify the type of distribution (normal, uniform, etc.) and then locate the corresponding row for your desired range of values. The value of P will be listed in the column for that range.

3. What does "find X" mean in "-aux.03 P(X-x) find X"?

In this expression, "X" represents a continuous variable. "Find X" means that you are being asked to determine the specific value of X that corresponds to a given probability or range of probabilities. This can be done by using a probability distribution table or a statistical software program.

4. Can I use any probability distribution table to find the value of P and X in "-aux.03 P(X-x) find P, find X"?

No, you will need to use a probability distribution table that corresponds to the specific type of distribution mentioned in the expression. For example, if the expression refers to a normal distribution, you will need to use a normal distribution table. Using the wrong table may lead to incorrect results.

5. How do I interpret the results of "-aux.03 P(X-x) find P, find X" in the context of my research?

The results of this expression represent the probability of an event occurring within a specific range of values for a continuous variable, as well as the specific value of that variable. In the context of your research, you can use this information to make informed decisions or draw conclusions about your data, such as identifying the likelihood of certain outcomes or making predictions.

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