What is the expected time between bites in a jungle full of bees?

In summary, the probability of getting bitten in a single second is equal to 0.2 given that a bee lands on you with a probability of 0.5. The distribution that deals with the number of trials before a success is a binomial random variable, where k is the number of bites and n is the number of seconds. To calculate the expected time between successive bites, we would use the binomial probability distribution with q = P(A and B).
  • #1
janela
4
0
You are in a jungle, at each second a bee lands on your arm with a probability of 0.5. Given that a bee lands on you, it will bite your arm with a probability of 0.2 and not do anything with a probability of 0.8, independently of all other mosquitoes. What is the expected time between successive bites?
 
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  • #2
1) What is the probability that you will get bitten in a single second.

2) What distribution deals with the number of trials before a success?

3) Show some working if you want help
 
  • #3
1) What is the probability that you will get bitten in a single second.

The probability of getting bitten (event B), given the bee lands on you (event A),
is given as P(B|A)=0.2
and P(A) is given as =0.5
is it correct to say P(A|B) = P (A and B) / P(A) and solve for P(B) ,
I am not sure how to solve for P(B) though, Bayes rule? 2) What distribution deals with the number of trials before a success?
Is this asking whether it is a binomial random variable
where k is the # of bites, n is the number of seconds (as each second is a new trial)
and Px(k) = (n C k) p^k * (1-p)^(n-k)

should the correct random variable equation should be
=(nCk) * P(B)^k (1-P(B))^(n-k)

I am not sure if it makes sense to make the number of bites equal to the number of seconds to find the E[X] time between successive bites.
(both equal to 2?)
 
Last edited:
  • #4
You are on the correct path with the conditional prob. What you are looking for is q = P(A and B), which is the binomial probability of being bitten.
 

What is a Probability Mass Function (PMF)?

A Probability Mass Function (PMF) is a mathematical function that describes the probability of a discrete random variable taking on a specific value. It assigns a probability to each possible outcome of a random variable.

How is a PMF different from a Probability Density Function (PDF)?

A PMF is used for discrete random variables, while a PDF is used for continuous random variables. A PMF assigns probability values to specific outcomes, while a PDF gives the relative likelihood of a range of values occurring.

What is the relationship between a PMF and a cumulative distribution function (CDF)?

A PMF and a CDF are related because the CDF is the cumulative sum of the PMF. The CDF gives the probability that a random variable is less than or equal to a specific value, while the PMF gives the probability of the random variable being exactly equal to that value.

How is a PMF used in practical applications?

A PMF is used in many practical applications, such as in statistics, economics, and engineering. It can be used to model and analyze data, make predictions, and evaluate the likelihood of certain outcomes.

What are some common examples of PMFs?

Some common examples of PMFs include the binomial distribution, the Poisson distribution, and the geometric distribution. These distributions are used to model different types of discrete random variables, such as the number of successes in a series of trials, the number of events in a given time period, and the number of trials until a success occurs.

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