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Let Y be a random variable with 𝑃[𝑌=𝑦]=C/3^y for y= 2, 3,4,…… What is the value of C?...

Question

Let Y be a random variable with 𝑃[𝑌=𝑦]=C/3^y for y= 2, 3,4,…… What is the value of C?

Let Y be a random variable with 𝑃[𝑌=𝑦]=C/3^y for y= 2, 3, 4,…… What is the value of C?



Answers

If $\frac{3}{4} y=6-\frac{1}{3} c,$ then what is the value of $2 c+\frac{9}{2} y ?$

We haven't given any question that see is a questo to buy three multiplied by X minus way, and we need to solve for y. So we need to find a fellow fight for forced letters. Cross multiply. So if a Grossman primary Jack three C is equal toe X minus way multiplied by a what, so here we get three c is equal to nothing but two x minus. Great, no bringing works Desert you get three C minus. The works is because toe minus two white and this can also before American is that Do I multiplying with negative? Sign his because toe to X minus three C. Now again, if you solve it, we get by reason off to advise toe two X minus three C divided by two hands if we find a value off by the Vallo. Fires to multiplied by X minus three. Diplomacy divided by

It's clear. So when you right here. So we know that one too. See, it's bigger than zero. The function is continuous and non negative, so integral from zero to see for four. Eat the negative two x t x is equal to one. When we evaluate this in general, this becomes four times and they could everyone have e to the negative to X from zero to see which is equal to negative to e. It's a negative to see plus two, which is equal to one. We got negative to e to the negative to see, to be equal to negative one. We've got negative to see to be equal to negative hell enough to so C is equal to Alan up to over two.

He has clear. So when you right here. So we know that when the sea is bigger than three, the function is continuous and non negative. So to fulfill the third condition, we go from the integral from three to see one over six x t x is equal to one. When we evaluate this integral, we get this to be cool to 16 square over too. Three to see which is equal to see square over 12 finest reports which is equal to one. We get to see square to be 21 so C s to be equal to square root of 21.

All right. So this is definitely a two part problem. It says if three Y equals Y plus two, What is the value of 2? Why? So the first thing that you need to do is solve for Y. And then once you know the value why you're going to plug it in to the other equation given. All right. So first things first. Let's solve for why? Using that first equation, we have three, Y equals Y plus two. And you just got to solve for Y by subtracting why? On those sides, That's going to give us two. Y equals two. And then you could finish solving by dividing both sides by two. Two, divided by two is one. So that's going to get why by itself. Again, two divided by two is one. So that's going to leave you with Y equals two. Now we are not done yet. The last thing we need to do is find what to Y is. So if we know why equals two, you could just plug it in. You have two times two. So your answer is going to be four or answer choice D.


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