Discrete random variables help?

1. Suppose a random variable X can equal 1, 2, 3, 4, or 5. If P(X<3)=0.4 andP(X>3).

"...and P(X>3)" is equal to... what?


2. If Y denotes the smaller of two numbers rolled on a pair of dice, determine the probability distribution of y. If the two numbers are equal then use the common number for the value of Y.

3. A pair of dice is rolled. Find (a) the expected value of the sum of the two numbers and (b) the standard deviation of the sum.

4. Four fair dice are rolled. Find the probability that (a) the number 6 appears at least twice and (b) the number 6 appears exactly once.


5. Assume X is a binomial random variable with an expected value of 4 and a variance of 2.4 Find (a) P(X=0) and (b) P(X=12).
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What sorts of results can one obtain upon rolling two dice? (Also, are we assuming that these are standard six-sided dice?) ;)
 
I have some practice problems for an upcoming quiz and really need some help on how to do them...
1. Suppose a random variable X can equal 1, 2, 3, 4, or 5. If P(X<3)=0.4 and P(X>3)=0..5
Find P(X=3) and P(X<4).


If that is now correct then
we know that \(\displaystyle \mathcal{P}(X<3)+\mathcal{P}(X=3)+\mathcal{P}(X>3)=1\) now solve for \(\displaystyle \mathcal{P}(X=3)\).

Also \(\displaystyle \mathcal{P}(X<3)+\mathcal{P}(X=3)=\mathcal{P}(X<4)\).
 
Thank you! Number 1 makes much more sense now that I know where my answers came from.
 
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