# Questions tagged [bayes-theorem]

For questions related to Bayes' theorem, a result about conditional probabilities.

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### Probability apple is delicious given a red apple is produced in a green apple orchard?

An example scenario of what I am trying to model: A farmer has a large apple farm, producing green apples (C=baseline apple color ?). Sometimes, a red one is produced (B=apple is red). I am wondering ...
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### Likelihood of Bayes' theorem [closed]

When estimating the parameter (hypothesis), I thought it was correct to compare the values of "P(hypothesis_i | observed data)" by changing i for each hypothesis However, when applying Bayes'...
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### Experimental Design: Selecting value of $n$ given desired width of credible interval

Suppose I have $n$ IID Bernoulli trials with $k$ successes. Assume that as a prior we are assuming that $P(\theta)$ is uniform on $[0,1]$. We can pretty easily use Bayes theorem to represent the ...
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1 vote
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### Gaussian as mixture with uniform weights

Suppose $W$ is $\operatorname{Uniform}[0,1]$ distributed. Suppose $Y|W$ has known mean $\mu(W)$ and variance $\sigma^2(W)$, where $\mu$ and $\sigma$ satisfies some regularity conditions: (1) $\mu$ and ...
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### Need Clarity in Finding Expectation of X, and Y

If there are four buses each bus has 40,33,25,50 students respectively. If X,Y are two random variables, X represents the no of students in the bus of the selected student , Y represents the no of ...
15 views

### Deriving posterior distribution with explicit constants in closed form using Jacobian method compared to Bayes' rule

Question on Bayesian Inference Deriving posterior distribution with explicit constants in closed form using Jacobian method compared to Bayes' rule I am working on a Bayesian ...
1 vote
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### Solving the marginal likelihood integral and approximating closed-form solutions for that

Given the likelihood function: $p_{y_s|r_s,x}(y_s|r_s,x) = \frac{1}{\sqrt{2\pi}} e^{-\frac{(y_s - \alpha \frac{\rho_s}{r_s^4})^2}{2}}$ and the prior distribution for $$r_s$$: \[ p_{r_s}(r_s) = \...
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### Best strategy to determine which of two coins is biased using only two flips

We have two coins - one fair, and one biased with a probability of 0.6 for flipping a head. We get to make exactly two flips before making a guess as to which coin is biased. The question is which ...
1 vote
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### I don't understand why this solution used Bayes Theorem instead of the regular formula for conditional probability. [closed]

When I view the solution to this problem, I understand the calculations but I don't understand why those calculations were done. Below is the question that I'm reading A theme park conducts a study ...
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### Simple example of Bayesian probability, picking from a bucket

Bowl I contains six red chips and four blue chips. Five of these 10 chips are selected at random and without replacement and put in bowl II, which was originally empty. One chip is then drawn at ...
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### Apply Bayes' Rule to a joint, prior distribution?

The problem is how to update a joint prior distribution consisting of two independent variables with observed evidence? For the prior distribution, data exists for average event frequency (i.e., ...
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### How to get an intuitive viewpoint towards Bayes theorem

At the time of shuffling 52 playing cards, 5 cards are dropped accidentally. If it is known that 2 of 5 cards are red, find probability that all dropped cards are red cards. I cannot seem to ...
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1 vote
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### Question 29 from Chapter 3 of A first course to probability from Sheldon Ross ed. 10

Xiku Road has $n_1$, $n_2$, $n_3$, and $n_4$ houses with $1$, $2$, $3$, and $4$ occupants, respectively. Two random selection without replacement strategies are being contemplated to obtain a sample ...
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### Conditional Probability in Selection of Nuts from Different Weight Distributions

I'm struggling with solving a problem involving conditional probability. Here's the problem: There are three species of nuts: those from the canton of St. Gallen (Switzerland), whose weight in grams ...
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### Bayes' formula for distriibutions

In my statistics course, we have discussed Bayes' theorem for distributions: $$p(\theta | y)=\frac{p(y|\theta)p(\theta)}{\int p(y|\theta)p(\theta) \mathrm{d}\theta}$$ Where $p(\theta)$ is the prior ...
1 vote
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### Calculate the posterior distribution

How can I solve the letter (a)? Discrete sample spaces: suppose there are N cable cars in San Francisco, numbered sequentially from $1$ to $N$. You see a cable car at random; it is numbered $203$. You ...
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