# discrete random variable hw problem

#### lilmissr

##### New member
Hi everyone, I am new to the forum.
I am doing a class of statistics and prob and not a math major! struggling horribly.

I have 2 hw problems I need help getting started with. Any insight into the concept of Discrete RV would help too! Thanks for anyones time or help!

-Suppose a fair dice is tossed three times. Let X be the largest of the three faces to appear. Find px (k).
*I kno that the sum must be 216 if it was 6 each time, but I don't know how to present that in this concept.

-Suppose x is a binomial random number with n=4 and p=2/3. What is the pdf of 2X+1?
*I have no idea how to start this or what the PDF really is?

Any help would really be appreciated! I have a test this Thursday and I am really stuck!

#### arthur ohlsten

##### Full Member
I will do the 1st. I also do not know what pdf means. I suggest you place the second question back on the site and perhaps someone will help

3 dice have 6x6x6=216 possible sums

how many ways may a 1 be the largest of the three faces? 1 way
no of 1's largest=1

how many ways for a 2? The total number of ways a number no greater than a 2 may appear is 2x2x2=8. But one of these 8 ways is the three ones ,or maximum face value 1. Thus only 7 ways
no of 2's largest=7

how many ways for a three to be largest? total ways no face greater than 3 is 3x3x3=27 ways
but 1 of these is no face greater than 1, and 7 faces no greater than 2. Thus only 27-1-7
no of 3 largest = 19

how many ways for a 4 to be greatest? total ways no face greater than a 4 = 4x4x4=64. But one of these is a face nogreater than a 1 ,7 faces no greater than a 2 and 19 faces no greater than a 3. Thus only 64-1-7-19=37
no of 4 largest=37

how many ways a 5 to be greatest? ( I will do it leaving out the verbage)
total=5x5x5=125
125-1-7-19-37=61
no of 5's largest=61

6 greatest
6x6x6=216
216-1-7-19-37-61=91
no of 6 greatest=91

P(1)=1/216
P(2)=7/216
P(3)=19/216
P(4)=37/216
P(5)=61/216
P(6)=91/216

Arthur

#### Subhotosh Khan

##### Super Moderator
Staff member
lilmissr said:
Hi everyone, I am new to the forum.
I am doing a class of statistics and prob and not a math major! struggling horribly.

I have 2 hw problems I need help getting started with. Any insight into the concept of Discrete RV would help too! Thanks for anyones time or help!

-Suppose a fair dice is tossed three times. Let X be the largest of the three faces to appear. Find px (k).
*I kno that the sum must be 216 if it was 6 each time, but I don't know how to present that in this concept.

-Suppose x is a binomial random number with n=4 and p=2/3. What is the pdf of 2X+1?
*I have no idea how to start this or what the PDF really is? Probability Distribution Function

Any help would really be appreciated! I have a test this Thursday and I am really stuck!