# Thread: Expected value, variance and standard deviation

1. ## Expected value, variance and standard deviation

Hi could someone help me with this question
I already found that a) is 21/4 and c) is 297/48 but how do you find b) for Pr(X<m)

Thanks

2. ## Re: Expected value, variance and standard deviation

just find the pmf, and then discretely integrate this to determine the cdf

3. ## Re: Expected value, variance and standard deviation

I am only 12 and my teacher didn't tell me how to do that, could you please explain it a bit more simply

4. ## Re: Expected value, variance and standard deviation

Originally Posted by ChanelSapphire
I am only 12 and my teacher didn't tell me how to do that, could you please explain it a bit more simply
Do you know what a probability mass function is?

Can you list the set of possible events and determine for each what the value of $X$ is?

Can you determine the probability of each of these events?

5. ## Re: Expected value, variance and standard deviation

Originally Posted by ChanelSapphire
Hi could someone help me with this question
I already found that a) is 21/4 and c) is 297/48 but how do you find b) for Pr(X<m)
$\{(h,1),~ (h,2),~(h,3),~(h,4),~(h,5),~(h,6),~(t,2),~(t,4),~( t,6),~(t,8),~(t,10),~(t,12)\}$
$\mathscr{P}(X=1)=\dfrac{1}{12}$ WHY?
$\mathscr{P}(X=2)=\dfrac{2}{12}$ WHY?
$\begin{array}{*{20}{c}} {\mathcal{P}(X = ?)}&|&{\_\_\_} \\ \hline {\mathcal{P}(X = 1)}&|&{\_\_\_} \\ {\mathcal{P}(X = 2)}&|&{\_\_\_} \\ {\mathcal{P}(X = 3)}&|&{\_\_\_} \\ {\mathcal{P}(X = 4)}&|&{\_\_\_} \\ {\mathcal{P}(X = 5)}&|&{\_\_\_} \\ {\mathcal{P}(X = 6)}&|&{\_\_\_} \\ {\mathcal{P}(X = 8)}&|&{\_\_\_} \\ {\mathcal{P}(X = 10)}&|&{\_\_\_} \\ {\mathcal{P}(X = 12)}&|&{\_\_\_} \\ \end{array}$