Bernoulli distribution. Problem with finding 'k' in formula.

[JujiGatame]

Hello everyone!

Here is the task that I have problem solving.

We roll the dice 4 times. Determine a random variable that describes k times will fall 6. Calculate expectation and variance.

I know that:
X - "counts how many times has fallen 6"
R(X) = {0, 1, 2, 3, 4}
n = 4
p = 1/6
q = 5/6

I know how to get expectation and variance, but I don't know how to get this k in formula.

 

[LCKurtz]

You have [imath]X =[/imath] number of times [imath]6[/imath] occurs in [imath]4[/imath] trials and, as you have indicated,[math]P(X=k) = \binom 4 k \left( \frac 1 6\right)^k \left(\frac 5 6\right)^{4-k},~k=0..4[/math]You have indicated you know how to calculate the mean and standard deviation of [imath]X[/imath]. Those are your answers for the random variable [imath]X[/imath]. The [imath]k[/imath] in your formula is just a dummy variable and you wouldn't expect it to appear in your answer.

 

[Deleted member 4993]

Hello everyone!

Here is the task that I have problem solving.

We roll the dice 4 times. Determine a random variable that describes k times will fall 6. Calculate expectation and variance.

I know that:
X - "counts how many times has fallen 6"
R(X) = {0, 1, 2, 3, 4}
n = 4
p = 1/6
q = 5/6

I know how to get expectation and variance, but I don't know how to get this k in formula.

Please post the EXACT and COMPLETE problem as it was presented to you.