1. ## Discrete Random Variables

Hi. Glad to see that we're being reminded of the rules. Here's a question on random variables.

The discrete random variable X has a probability density function

$\displaystyle P(X=x)= \frac{x}{10} where x= 1, 2, 3, 4$

P(X=x) is 0 otherwise

If $\displaystyle Y$denotes the sum of two independent observations of $\displaystyle X$
Determine the value of $\displaystyle P(Y=4)$

2. Originally Posted by I-Think
The discrete random variable X has a probability density function$\displaystyle P(X=x)= \frac{x}{10} where x= 1, 2, 3, 4$
P(X=x) is 0 otherwise
If $\displaystyle Y$denotes the sum of two independent observations of $\displaystyle X$
Determine the value of $\displaystyle P(Y=4)$
Note that elementary event Y=4 is simply {(1,3),(3,1),(2,2)}.
Calculate the probabilities of each and add.

3. Silly statistician, integration is for continuous random variables.

Sorry about this question, for some strange reason I thought this was a continuous random variable, and continued in this erroneous belief even after your help.

Oh well, everybody makes mistakes in life, and maths.