1) At the moment you just have probability statement. You should provide an actual probability (plug into the pmf).
2) You want to recall that if $X,Y$ are iid, then the sum follows a negative binomial distribution,
$$X+Y\sim \text{NB}(r = 2, p).$$
Further, we have that, assuming the support for...
The bottom 2 steps confuse me. X , Y has geometric distribution, I thought the formula for the mass function is (1-p)^k-1*p? How come your answer is (1-p)^k*p? Also, lots of textbooks use another formula for negative binomial distribution, when I use that formula, the answer is 1/(n-1). I am so confused. Please help！
If the possible values of $X$ and $Y$ are $\{0,1,2,3,\dotsc\}$, then $P(X = k) = (1-p)^{k} p$. If the possible values are $\{1,2,3,\dotsc\}$, then $P(X = k) = (1-p)^{k-1}p$. Instead of memorizing formulas, you should try to understand what they mean. In the first case, $X$ counts the number of failures until the first success; in the second, it counts the number of trials.
The same can be said about the negative binomial distribution.
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Twelve independent random variables, each uniformly distributed over the interval (0, 1], are added, and 6 is subtracted from the total. Determine the mean and variance of the resulting random variable.
The number of claims Z lodged in insurance company on each working day is Poisson random variable with parameter λ: P(Z = k) = λ k k! e −λ , k = 0, 1, 2, . . . . What is the distribution of the number of claims lodged during n working days? Prove your answer.
i thought the answer is just the sum of lambas, but is that this easy?
Discussion between probablyme and Yil…
Discussion between probablyme and Yil…