# [SOLVED]P(X-x) find P, find X, from table

#### karush

##### Well-known member
The probability distribution of the discrete variable X is given by the following table
View attachment 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

Staff member
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?

#### karush

##### Well-known member
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 $p=1-(0.4+0.2+0.07+0.02)=.31$

#### MarkFL

Staff member
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

##### Well-known member
Yes, that's correct.

Now, to find the expect value, find the sum of the products of the x-values and their corresponding probabilities.
$$\displaystyle (1\times0.4)+(2\times.31)+(3\times0.2)+(4\times0.07)+(5\times0.02)=2$$

#### MarkFL

Staff member
$$\displaystyle (1\times0.4)+(2\times.31)+(3\times0.2)+(4\times0.07)+(5\times0.02)=2$$
I get a slightly higher value...are you rounding because $X$ is given as discrete?

#### karush

##### Well-known member
uhmmm, well, don't recall any rounding. just let the WF compute it.

no sure what is meant by discrete

#### MarkFL

Staff member
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

Staff member
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

##### Well-known member
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