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We know that Beta distribution is conjugate prior for binomial likelihood. … So, it will be helpful if anyone can explain the reason for using beta likelihood instead of binomial and why do we get different distribution with binomial and beta likelihood? …

Is the covariance between number of success and failure in a binomial distribution with parameters n and p, the same as the covariance between two binomial variables, which is -np(1-p)? …

So for this question do I just need to state the assumptions for a binomial distribution? …

Next consider a sum of random number of random variables $W_N\equiv\sum_{i=1}^NY_i$, where $N\sim Binomial(n,q)$ ($n>1$ is a number or trials, and $q$ is success probability). … . $$ Additionaly I have information that $q=0.36$ and I am asked about a value of $\alpha$, for which $W_N$ is distributed as binomial. …

For X > 7, since the binomial distribution has .45920 I subtract that from 1, and use X <= 8 for X < 9, that value is .64437 (1 - .45920)/(.64437) = .839269 Wrong answer. …

Model this with a binomial distribution: 1)?= E[X] 2)?=Var[X] 3)?=P(X = 15) 4)? …

This is a mixture binomial distribution question. I know how to get the $\mu$ and $\sigma^2$ of the mixture, but I am not sure how to use it to get the probably of specific number. … Question: States that $X_1=B(2,0.52), X_2=B(3,0.41), X_3=B(4,0.38)$ are binomial distributions with 43%, 36%, 21% users respectively. Find the probability that occurrence is more than 2. …

What I have tried: My first instinct was to go to Calc>Binomial distributions> Binomial to get the graph of it. 2 questions: What does the question mean it needs values less than 21? … What is the purpose of the code that says "Random 25 c1; binomial 25 0.8"? Am I supposed to be input this code somewhere? …

Should I use the binomial distribution? …

We are given the following equality: $B(k;n,p)=B(k;n+1,p) + pb(k;n,p)$ where $B$ is the binomial cdf, $b$ is the binomial pdf, $n$ is the number of trials and $p$ is the probability of success. …

I have a Poisson approximation to binomial question, posted below. I'm not too sure if I'm using the proper formula: $$P(x) = e^{-np}(np)^x/x!$$ . … Use and justify Poisson approximation to Binomial. What I'm doing: $$P(x) = e^{-140 (.05)}(140*.05)^2/2!$$ . …

Say we have a binomial random variable $B \sim \operatorname{Bin}(n,p)$ and $n$ i.i.d. Normal random variables $N_i \sim N(p, 100)$. What is the distribution of $\sum_{i=1}^B N_i$? …

How to plot the binomial distribution for p = 0.3, p = 0.5 and p = 0.7 and the total number of trials n = 60 as a function of k the number of successful trials. …

Calculation of $EX$ using the binomial expansion formula is easy: \begin{align} EX &= \sum_{x=0}^{n}x\frac{n!}{(n-x)!x!}p^{x}(1-p)^{n-x}\\& = np \sum_{x=1}^{n}\frac{(n-1)!}{(n-x)!(x-1)!} … p^{x-1}(1-p)^{n-x}\\& = np(p+(1-p))^{n-1}\\& = np \end{align} How do I calculate $EX^2$ using the binomial expansion formula? …

+X_{n}$ I know that $Y_{n}$ is a Binomial distribution with $n \theta$ as expected value and $n \theta (1-\theta)$ as variance but I can't figure out the probability distribution of $n-Y_{n}$ and how …